Question

if x-1/x=3+2root2 find the value of x cube - 1/xcube​

Answer 1

Answer:

It is given that,

x=2−3

so,

1/x=1/(2−3)

By rationalizing the denominator, we get

=[1(2+3)]/[(2−3)(2+3)]

=[(2+3)]/[(22)−(3)2]

=[(2+3)]/[4−3]

=2+3

Now,

x−1/x=2−3−2−3

=−23

Let us cube on both sides, we get

(x−1/x)3=(−23)3

x3−1/x3−3(x)(1/x)(x−1/x)=243

x3−1/x