1 If a = p^1/3-p^-1/3
prove that: a^3 + 3a = p - 1/p

Mathematics

angeline2004 · 12.08.2020 04:01

ANSWER(S): 1 Show answers 8 Сomment

ANSWER(S)

answered: krazyykay

28.06.2019 13:40

p = 6s

step-by-step explanation:

answered: savdeco

28.06.2019 10:00

step-by-step explanation: s

answered: xcji7384

26.06.2019 21:20

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a) |-1|, |3/2|, |-2|, |-3|, |3.5|

answered: annyarias3563

30.01.2022 20:25

Hello, please consider the following.

We know that

$a = p^{\frac{1}{3}}-p^{-\frac{1}{3}}\\\\=p^{\frac{1}{3}}-\dfrac{1}{p^{\frac{1}{3}}}$

And we can write that.

$(p-\dfrac{1}{p})^3=(p-\dfrac{1}{p})(p^2-2+\dfrac{1}{p^2})\\\\=p^3-2p+\dfrac{1}{p}-p+\dfrac{2}{p}-\dfrac{1}{p^3}\\\\=p^3-\dfrac{1}{p^3}-3(p-\dfrac{1}{p})$

It means that, by replacing p by $p^{1/3}$

$(p^{1/3}-\dfrac{1}{p^{1/3}})^3=p-\dfrac{1}{p}-3(p^{1/3}-\dfrac{1}{p^{1/3}})\\\\\\\text{ So }\\\\a^3=p-\dfrac{1}{p}-3a\\\\\boxed{ a^3+3a=p-\dfrac{1}{p} }$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Other questions on the subject: Mathematics

Drag each scenario to show whether the final result will be greater than the original value, less than the original value, or the same as the original value. 1. a 25% decrease foll...

Mathematics

20.06.2019 18:04

3 answer(s)

mtunes

Plz need answer now will mark which situations represent linear functions? check all that apply. a)the temperature rises and falls over the course of a day. temperature is a funct...

Mathematics

21.06.2019 14:00

3 answer(s)

skye2598

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers,...

Mathematics

21.06.2019 19:20

2 answer(s)

cody665

At the beginning of 1974/75,2 years a man invested #2000 in a bank at 12.5% compound interest, if it degree #650 at the end of each two years to pay his son's school fees, after pa...

Mathematics

21.06.2019 19:30

3 answer(s)

aljdones

Urgent! 20 points! here is a you are the new manager at trusty goods wholesale produce. you need to figure out how to adjust the amount of produce in your notes after the events...

Mathematics

22.06.2019 00:00

1 answer(s)

rmans22209

What is the equation of a line, in general form, that passes through point (1, -2) and has a slope of 1/3 3x - y - 7 = 0 x - 3y + 7 = 0 x - 3y - 7 = 0...

Mathematics

22.06.2019 06:50

1 answer(s)

Fireburntbudder

Find the equation in standard form , of the line passing through points (2,-3) and (4,2)...

Mathematics

22.06.2019 09:00

1 answer(s)

Nathaliasmiles

Y=x+2 y=−x+8 what is the solution for this system of equations? enter your answer in the box (3,5) (5,0) (0,5) (2, 8)...

Mathematics

22.06.2019 09:00

2 answer(s)

fgcherubin

Can someone me with this i am confused and need
Can someone me with this i am confused and need

...

Mathematics

22.06.2019 10:10

1 answer(s)

cvhufjbvbcxx9845

Match the linear equations with their x- and y-intercepts. (-20/3, 0) and (0, 4) (3, 0) and (0, -21) (-15/3, 0) and (0, 4) (-7/3, 0) and (0, 7/3) (2, 0) and (0, -1) equation interc...

Mathematics

22.06.2019 10:30

3 answer(s)

brown62

Δabc is located at a (2, 0), b (4, 4), and c (6, 3). zackery says that δabc is an isosceles triangle, while verna says that it is a right triangle. who is correct? a. zackery, bec...

Mathematics

22.06.2019 12:00

1 answer(s)

Lalagrl

The diameter of a basketball is 9.39 inches. which is closest to the number of square inches of material used in constructing a basketball? a. 118 square inches b. 277 square in...

Mathematics

22.06.2019 12:00

3 answer(s)

goargrant

Load more questions: Mathematics Else questions

1 If a = p^1/3-p^-1/3prove that: a^3 + 3a = p - 1/p

Other questions on the subject: Mathematics

1 If a = p^1/3-p^-1/3
prove that: a^3 + 3a = p - 1/p