Question

If a = root 2-1, find the values of (a- 1/a) cube​

Answer 1

$\sf\underline\purple{Given:-}$

$\sf a=√2-1$

$\sf \frac{1}{a}=\frac{1}{√2-1}$

$\sf\underline\purple{To \:\: Find:- }$

$\sf a-\frac{1}{a}=?$

$\sf\underline\purple{Solution}$

$\sf a=√2-1$

$\sf \frac{1}{a}=?$

$\sf \frac{1}{√2-1}×\frac{√2+1}{√2+1}$

$\sf \frac{√2+1}{1}$

$\sf [√2-1-(√2+1)]³$

$\sf [-2]³=-8$

$\sf [a-\frac{1}{a}]³=-8$