Question

If y-(1/y)=x then what is y^3-(1/y^3)=?

Answer 1

Answer: y3−1y3=234

Step-by-step explanation:

y−1y=6

(y−1y)3=63

y3−3y+3y−1y3=216

y3−1y3=216+3(y−1y)=216+3(6)

not sure:)

Answer 2

Answer:

So we start with

y - (1/y) = x

if we cube both sides we get

y^3 - 3y^2*(1/y) + 3y*1/(y^2) - 1/(y^3) = x^3

which is the same as

y^3 - 1/(y^3) = x^3 + 3y^2*(1/y) - 3y*1/(y^2)

which is equal to

y^3 - 1/(y^3) = x^3 + 3y - 3*(1/y)

and since x = y - (1/y), that means 3x = 3y - 3*(1/y). So we can substitute 3x into the equation and we get:

y^3 - 1/(y^3) = x^3 + 3x

And that's your answer.