Question

if x^2+1/x^2 =8^3 find the value of (x^3-1/x^3)​

Answer 1

Solution :

We know that: (x- y)^2 = x^2 + y^2 - 2xy

Replace y with 1/x, we get

(x-1/x)2 = x^2 + 1/x^2 - 2

Since (x2 +1/x^2) = 8^3 (given)

(x-1/x)^2 = 512+17 = 529

or (x-1/x)= ± 23

Now, Find x^3 - 1/x^3

We know that, x^3- y^3 = (x-y)(x^2+y^2+ xy)

Replace y with 1/x, we get

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

Use (x-1/x) = 23 and (x2 + 1/x^2) = 512

x^3-1/x^3 = 23 x 512 = 11776

x^3-1/x^3 = 11776