Fundamental Drill#1

Algebra Level 3

$\large x\left(\sqrt x - \frac 1{\sqrt x}\right)\left(\sqrt x+ \frac 1{\sqrt x}\right)=15$

Find the number of real solutions to the equation above.

You can try more of my fundamental problems here .

0 4 1 2

1 solution

Donglin Loo
Jun 19, 2018

$x(\sqrt{x}-\cfrac{1}{\sqrt{x}})(\sqrt{x}+\cfrac{1}{\sqrt{x}})=15$

$x([\sqrt{x}]^2-[\cfrac{1}{\sqrt{x}}]^2)=15$

$x(x-\cfrac{1}{x})=15$

$x^2-1=15$

$x^2=16$

$\because \sqrt{x}$ is in the original equation.

$\therefore x\geq0$

$\therefore x=4$ is the only solution and $x=-4$ is unsuitable.

$\therefore$ the number of real solution is $\boxed{1}$ .