Question

Find the square root of ${(x+\frac{1}{x})}^2-4(x-\frac{1}{x})$.

Answer 1

Now,

${(x+\frac{1}{x})}^2-4(x-\frac{1}{x})$

$={(x-\frac{1}{x})}^2+4-4(x-\frac{1}{x})$ [ Since $(a-b{)}^2=(a+b{)}^2-4ab$]

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

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

So square root of the given expression is $\pm (x-\frac{1}{x}-2)$.