Question

if x+1/x=root 2 evaluate x^3+1/x^3

Answer 1

Answer:

Step-by-step explanation: hi...

Answer 2

$x+\frac{1}{x} = \sqrt{2}$

We have the identity

$\large\black\boxed{(a+b)^2 = a^2+b^2+2ab}$

Using the above identity,

$(x+\frac{1}{x})^2 = {2}$

$x^2+\frac{1}{x^2}+2=2$

$x^2+\frac{1}{x^2}=0$

We have the identity

$\large\black\boxed{(a^3+b^3) = (a+b)(a^2+b^2-ab)}$

Using the above identity

$x^3+\frac{1}{x^3} = (x+\frac{1}{x})(x^2+\frac{1}{x^2}-1)$

Substitute known values

$x^3+\frac{1}{x^3} = \sqrt{2} *(0-1)$

$\huge\black\boxed{x^3+\frac{1}{x^3} = -\sqrt{2}}$