calculate without using tables the values of
(1+√2)⁴ - (1-√2)⁴​

Answers

Answer 1
Answer:  24*sqrt(2)

=========================================================

Work Shown:

A = 1+sqrt(2)

B = 1-sqrt(2)

-------------------

Using A and B, let's add and subtract those values

A+B = (1+sqrt(2))+(1-sqrt(2))

A+B = 1+sqrt(2)+1-sqrt(2)

A+B = 1+1+sqrt(2)-sqrt(2)

A+B = 2

and

A-B = (1+sqrt(2))-(1-sqrt(2))

A-B = 1+sqrt(2)-1+sqrt(2)

A-B = 1-1+sqrt(2)+sqrt(2)

A-B = 2sqrt(2)

-------------------

Next, square both sides of the A equation

A^2 = (1+sqrt(2))^2

A^2 = (1+sqrt(2))(1+sqrt(2))

A^2 = 1(1+sqrt(2))+sqrt(2)(1+sqrt(2))

A^2 = 1+sqrt(2)+sqrt(2)+sqrt(2)*sqrt(2)

A^2 = 1+2sqrt(2)+2

A^2 = 3+2sqrt(2)

-------------------

Do the same for B

B^2 = (1-sqrt(2))^2

B^2 = (1-sqrt(2))(1-sqrt(2))

B^2 = 1(1-sqrt(2))-sqrt(2)(1-sqrt(2))

B^2 = 1-sqrt(2)-sqrt(2)-sqrt(2)*(-sqrt(2))

B^2 = 1-2sqrt(2)+2

B^2 = 3-2sqrt(2)

There's a bit of nice symmetry going on with A^2 and B^2, due to A and B having similar symmetric structures themselves.

-------------------

Lets add A^2 to B^2

A^2+B^2 = (3+2sqrt(2)) + (3-2sqrt(2))

A^2+B^2 = 3+2sqrt(2) + 3-2sqrt(2)

A^2+B^2 = 3+3+2sqrt(2)-2sqrt(2)

A^2+B^2 = 6

-------------------

Now onto the final event

We'll use the difference of squares rule twice

Afterward, apply substitution using the previous sections above.

A^4 - B^4 = (A^2)^2 - (B^2)^2

A^4 - B^4 = (A^2-B^2)(A^2+B^2)

A^4 - B^4 = (A-B)(A+B)(A^2+B^2)

A^4 - B^4 = (2sqrt(2))(2)(6)

A^4 - B^4 = 2*6*2*sqrt(2)

A^4 - B^4 = 24*sqrt(2)

(1+sqrt(2))^4 - (1-sqrt(2))^4 = 24*sqrt(2)

-------------------

To check this with your calculator, you can type in the following

(1+sqrt(2))^4 - (1-sqrt(2))^4 - 24*sqrt(2)

The result you should get should be 0, or very close to it

I'm using the property that if x = y, then x-y = 0.


Related Questions

Please help me I really need it Big points for help.
The three Miller boys were calculating the volume of their new fish tank to determine how many gallons of water the tank can hold. Each brother measured a different dimension of the tank. Their measurements were 1 yard in length, 1 foot in width, and 18 inches in height.

1. There are approximately 7.5 gallons per cubic foot. If you want to know how many gallons of water the tank can hold, what unit of measure would you use to calculate the volume of the fish tank? Explain why

2. Determine how many gallons of water the fish tank can hold. Carefully show your work and include units of measure.​

Answers

1. Because you know the number of gallons per square foot. You would want to use cubic feet for the measurement of the tank.

2. Convert all dimensions to feet:

1 yard = 3 feet

18 inches = 1.5 feet.

Volume of tank = 3 x 1.5 x 1 = 4.5 cubic feet.

Multiply gallons per cubic foot by cubic feet of tank:

7.5 x 4.5 = 33.75 gallons.

If 2KL=KL+MN, then KL=MN

Choose the definition, theorem, or postulate that justifies the statement.

A. Subtraction Property of Equality
B. Definition of Midpoint
C. Segment Addition Postulate
D. Symmetric Property (of= or≅)
E. Reflexive Property (of= or≅)
F. Transitive Property (of= or≅)
G. Definition of Congruence
H. Substitution Property
I. Addition Property of Equality
J. Multiplication Property of Equality
K. Division Property of Equality

Answers

Answer:

a. subtraction property of equality

Step-by-step explanation:

Write an equation in slope-intercept form that passes through (2, -3) and slope of -5.

Answers

Step-by-step explanation:

Hey there!

The given slope is "-5" and it passes through point (2,-3).

Use one-point formula to find out the equation.

[tex](y - y1) = m(x - x1)[/tex]

Put all values.

[tex](y + 3) = - 5(x - 2)[/tex]

Simplify it.

[tex](y + 3) = - 5x + 10[/tex]

[tex]y = - 5x + 10 - 3[/tex]

[tex]y = - 5x + 7[/tex]

Therefore, the equation is y= -5x+7.

Hope it helps...

drag each item to its correct place es de monomios​

Answers

Answer:

Step-by-step explanation:

-2x

Grado : 1

Coefficiente  : -2

Parte literal :   x

x²y⁴:

Grado : 2+4 = 6

Coefficiente  : 1

Parte literal :   x²y⁴

Solve the inequality:

u^2 > 8u + 33

Answers

Answer:

u<−3 or u>11

Step-by-step explanation:

u2=8u+33

u2−(8u+33)=8u+33−(8u+33)(Subtract 8u+33 from both sides)

u2−8u−33=0

(u+3)(u−11)=0(Factor left side of equation)

u+3=0 or u−11=0(Set factors equal to 0)

u=−3 or u=11

Can y’all please help me with my question??

Answers

Answer:

p

Step-by-step explanation:

Can y’all please help me with my question??

pretty sure it’s x^10=x^p

5. It is a method of describing a set, in words.
A. Roster Notation
C. Set Builder Notation
B. Listing Method
D. Verbal Description Method​

Answers

The correct answer choice is D. Hope this helps!!

Answer

There are two common ways of describing or specifying the members of a set: roster notation and set builder notation. These are examples of extensional and intensional definitions of sets, respectively

50+ Points!

Solve the equation.

5^-9×325+(-42÷-14)

Answers

Answer:

−6347653.25 or 3.0001664, not my style of math but it is definitely one of the two.

Step-by-step explanation:

−1953125 x 325 + 3

−6347656.25 + 3 = −6347653.25

Answer:

3.0001664

Step-by-step explanation:

.

Triangle CDA is the image of triangle ABC after a 180° rotation around the midpoint of segment AC. Triangle ECB is the image of triangle ABC after a 180° rotation around the midpoint of segment BC.

Answers

Answer:ABCD and ABEC are parallelograms because they both have a pair of parallel lines.

DCE AND CEB are congruent angels

Best answer gets brainliest 2+2

Answers

Answer:

I would say this would be either 4, 22, or fish

A town has a population of 2000 and grows at 3.5% every year. To the nearest year, how long will it be until the population will reach 3900?

Answers

Answer:

27 years.

Step-by-step explanation:

2000->100%

?->3.5%

=70 people growth each year

3900-2000=1900[expected growth]

70-per year

1900-?

1900*1/70=27.1

=27.|1

27 years

It will take 9 years for the town's population to reach 3900.

What is an exponential function?

"An exponential function is a function of form f (x) = a^(x), where a is the base."

Exponential growth function:

f(x) = a×(1+r)^x

where,

f(x) = exponential growth function

a = initial amount

r = growth rate

x = number of time intervals

For given situation,

initial population: a = 2000,

growth rate r = 3.5/100

⇒ r = 0.035

f(x) = 3900

We need to find the nearest year to reach the population 3900.

i.e., to find value of x(years)

Using the exponential growth function,

⇒ 3900 = 2000(1 + 0.035)^x

⇒ 3900/2000 = (1.035)^x

⇒ 1.95 = (1,035)^x

⇒ [tex]x=log_{1.035} 1.95[/tex]

⇒ x = 19.41

⇒ x ≈ 19

Therefore, it will take 19 years to reach 3900.

Learn more about exponential growth here:

https://brainly.com/question/11487261

#SPJ2

in which of these situations do the quantities combine to make 0? A. A dolphin swims 20 feet straight down from the surface. It then rises 20 feet to return to the surface. B. Scott earns $20 at his family's garage sale. He then earns $20 walking dogs for his neighbors. C. Travis receives $10 from a friend to pay for a concert ticket. He then spends $20 on tickets for his friend and himself. D. A scuba diver drops 30 feet below sea level. He then swims 30 feet across the ocean floor.​

Answers

Answer:

A. A dolphin swims 20 feet straight down from the surface. It then rises 20 feet to return to the surface.

Step-by-step explanation:

It goes down 20 then up 20

-20 + 20 = 0

Answer:

Answer A

Step-by-step explanation:

This is the correct option as you are going feet down and then 20 feet back up. So basically, an equation that would represent this is -20+20=0.

Which expressions are equivalent to 3x + 3(x + y)?
Choose all answers that apply:
A 6x + 3y
B 3(x + x + y)
C 3ay

Answers

3x + 3(x + y)

3x + 3x - 3y

6x - 3y

your answer would be A

Answer:

A and B

Step-by-step explanation:

3x+3(x+y)

3x+3x+3y

6x+3y

B

3(x+x+y)

3x+3x+3y

6x+3y

The data represented by the following stem-and-leaf plot range from
to
2189
3 504
4 127
5 36
A. 29; 53
B. 28; 56
C. 28; 53
D. 29, 56
SUBMIT

Answers

Answer:

28;56

Step-by-step explanation:

According to the stem-and-leaf plot, the range of the data represented by the stem-and-leaf plot is 63.

To determine the range of the data represented in stem and leaf plot, we need to look at the smallest and largest values. The smallest value is obtained by taking the smallest leaf in the plot, which is 36, and adding it to its corresponding stem (5). So, the smallest value in the data set is 536.

Next, we look for the largest value, which is found at the bottom of the last stem. In this case, the last stem is 5, and the largest leaf is 9. Therefore, the largest value in the data set is 599.

Now that we have the smallest and largest values, we can calculate the range by subtracting the smallest value from the largest value:

Range = Largest Value - Smallest Value

Range = 599 - 536

Range = 63

So, the answer is Answer: C. 28; 53

To know more about stem and leaf plot here

https://brainly.com/question/32053953

#SPJ2

Please help and explain!! I WILL MARK BRAINLIEST

Answers

Answer:

plot a graph and count it

Step-by-step explanation:

midpoint is the middle point of the line. it can be found by dividing the length of the line by 2 then counting inwards by that number.

There are 2 out of 5 boxes shaded. What percent is not shaded?

Answers

Answer:

i am going to say 3/5 but  am not sure

Step-by-step explanation:

Jacob spent $10 of the $25 in his wallet write a decimal that represents the fraction of the $25 Jacob spent

Answers

She she suvsuzsuz sue sh Sejm sis sue si sue.

Finance Application. Tony earned $8.25 per hour at his after school job. Each week he earned $80. Write and solve an equation to show how many hours he worked each week.​

Answers

Answer:

  9.6969 hours

Step-by-step explanation:

8.25x = 80

x = 9.6969 hours

A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?

(x, y) → (x + 5, y – 3)
(x, y) → (x + 5, y + 3)
(x, y) → (x – 3, y + 5)
(x, y) → (x + 3, y + 5)

Answers

Answer:

The last one (x,y)->(x+3,y+5)

Step-by-step explanation:

Whenever you move the x coordinate it’s the opposite, for example translated 3 units the the left is +3 and translated 3 units to the right is -3.

Whenever you move the y coordinate it’s normal so up 5 units means +5 and down means -5.

Answer:

C

Step-by-step explanation:

simple addition

Select the smallest fraction from the following list of fractions.
3/4
2 2/3
3/5
1 1/2
7/8
2/3

Answers

Answer: 3/5

I’m not sure if you need an explanation
The answer is 3/5 your welcome

PLS ANSWER HELP
Thanks

Answers

Its congruent to ELG :)

How can I turn this into a graph in Desmos,

Answers

Answer:

in Desmos there should be a plus sign right above the list of your equations on the left side. Click that plus sign and then click "table". then enter your numbers. then your points will be shown on the graph

to turn this into a line long press on the button next "y" on the table you have made, then select "lines"

Answer:

you go to desmos and you go to the left side of the website. choose which graph you want to do. if you want to use a regression line graph, or anything else. lmk if you need help

Step-by-step explanation:

0.93=

please explain how you got the answer.

Answers

fraction form 93/100
percentage form 93%
theres many wayss you could write this but im not sure i surley understand what you mean by this question

Identify the number of terms in this polynomial.
5k^5+7k-2

Answers

Answer:

cuatro terminos

The figure shows three quadrilaterals on a coordinate grid: A coordinate plane is shown. Quadrilateral D has sides measuring 3 units and 1 unit. Quadrilateral F has sides measuring 3 units and 1 unit. Quadrilateral E has sides measuring 2 units and 6 units. Which of the following statements is true about the three quadrilaterals? D and E are similar but not congruent. E and F are similar and congruent. D and E are similar and congruent. F and D are similar but not congruent.

Answers

Answer:

A: D and E are similar but not congruent.

Step-by-step explanation:

hope this help

Rewrite the expression using a single, positive exponent: 14^-3x14^12

Answers

Answer:

14⁹

Step-by-step explanation:

When you're multiplying, you add the exponents. So, -3+12=9.

1. How can you tell the difference between the pre-image and image when only given the coordinates or a picture?

Answers

Answer:You need To tell them apart, they will usually be defined separately.

Step-by-step explanation:

i need help asap please

Answers

Answer:

270mi

Step-by-step explanation:

5.4/2 = 2.7

2.7 * 100 = 270

what equation represents the line that passes through (-2,-1) and has a slope of 5

Answers

Answer:

y + 1 = 5 (x+2)  in point slope form   or   y = 5 x + 9  in intercept slope form

Step-by-step explanation:

Answer:

y=5x+9

Step-by-step explanation:

Please help, due in 6 hrs (will mark brainliest and giving 85 points) will ask seperate question for the 85 points

Answers

Answer: If I'm being honest I only know parts A and B.

A. (4, 19) and (7, 7).

B. 4/1 or just 4.

Step-by-step explanation:

B. From point (7, 7) to (6, 11) is up 4 and left 1, rise over run is how you write the slope so it would be written as 4/1. Depending on you're teacher you can just put 4 and it can be correct, so, 4/1 or just 4.

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