Question

If, $a+\frac{1}{a}=6$ then, $a-$ $\frac{1}{a}=$

Answer 1

Given,

$a+$ $\frac{1}{a}$ $=6$

by squaring both side

$(a+\frac{1}{a}{)}^2=$$(6{)}^2$

$a^2+\frac{1}{a^2}+2a\frac{1}{a}=36$

$a^2+\frac{1}{a^2}+2=36$

$a^2+\frac{1}{a^2}=34$

$a^2+\frac{1}{a^2}-2=34-2$

$a^2+\frac{1}{a^2}-2a\frac{1}{a}=32$

$(a-\frac{1}{a}{)}^2=$$32$

$a-$ $\frac{1}{a}=$ $\sqrt{32}$

$a-$ $\frac{1}{a}=$ $4\sqrt{2}$