Question

Solve (i) $\sqrt{x}-\frac{1}{\sqrt{x}}$
(ii) $x^2-\frac{1}{x^2}$

Answer 1

$i).\sqrt{x}-\frac{1}{\sqrt{x}}$

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

$\Rightarrow {\left(x^{\frac{1}{4}}\right)}^2-{\left(\frac{1}{x^{\frac{1}{4}}}\right)}^2=(x^{\frac{1}{4}}-\frac{1}{x^{\frac{1}{4}}})(x^{\frac{1}{4}}+\frac{1}{x^{\frac{1}{4}}})$

$ii).x^2-\frac{1}{x^2}$

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

Hence, solved.