Question

If $x+\sqrt{x^2-9}=4$ then find the value of $x-\sqrt{x^2-9}$.

Answer 1

Given,

$x+\sqrt{x^2-9}=4$

or, $\frac{1}{x+\sqrt{x^2-9}}=\frac{1}{4}$

or, $\frac{x-\sqrt{x^2-9}}{(x{)}^2-(\sqrt{x^2-9}{)}^2}=\frac{1}{4}$

or, $\frac{x-\sqrt{x^2-9}}{9}=\frac{1}{4}$

or, $x-\sqrt{x^2-9}=\frac{9}{4}$.