Question

Solve the following equations:
$\frac{x+\sqrt{x^2-1}}{x-\sqrt{x^2-1}}+\frac{x-\sqrt{x^2-1}}{x+\sqrt{x^2-1}}=98$

• A. $\pm 1$
• B. $\pm 5$
• C. $\pm 10$
• D. $\pm 4$

Answer 1

Answer: (B)

$\pm 5$

Given, $\frac{x+\sqrt{x^2-1}}{x-\sqrt{x^2-1}}+\frac{x-\sqrt{x^2-1}}{x+\sqrt{x^2-1}}=98$

$\Rightarrow \frac{{(x+\sqrt{x^2-1})}^2+{(x-\sqrt{x^2-1})}^2}{(x+\sqrt{x^2-1})(x-\sqrt{x^2-1})}=98$

$\Rightarrow \frac{x^2+x^2-1+2x\sqrt{x^2-1}+x^2+x^2-1-2x\sqrt{x^2-1}}{x^2-(x^2-1)}=98$

$\Rightarrow 4x^2-2=98$

$\Rightarrow 4x^2=100$

$\Rightarrow x^2=25$

$\Rightarrow x=\pm 5$