Question

The value of $x\in R$ which satisfies the given equation $6\sqrt{\frac{x}{x+4}}-2\sqrt{\frac{x+4}{x}}=11$ is

• A. $\frac{4}{35}$
• B. $-\frac{4}{36}$
• C. $\frac{16}{3}$
• D. None of these

Answer 1

The correct option is D None of these

Let $\sqrt{\frac{x}{x+4}}=y.$ Then the given equation becomes
$6y^2-11y-2=0$ i.e. $y=-\frac{1}{6},2$
As $y=\sqrt{\frac{x}{x+4}}\ge 0$ so $y\ne -\frac{1}{6}$
$\Rightarrow y=2\Rightarrow \frac{x}{x+4}=y^2=4\Rightarrow x=-\frac{16}{3}$