Question

If $\frac{a}{c}-\frac{a}{b}=\frac{b-c}{a}$, with $a>0,b>0$, and $c>0$ what is the value of $a$ in terms of $b$ and $c$?

• A. $b-c$
• B. $\sqrt{bc}$
• C. $\sqrt{b-c}$
• D. $\frac{\sqrt{b-c}}{bc}$
• E. $\frac{\sqrt{bc}}{b-c}$

Answer 1

Answer: (B)

$\sqrt{bc}$

Given, $\Rightarrow \frac{a}{c}-\frac{a}{b}=\frac{b-c}{a}$
$\Rightarrow \frac{ab-ac}{bc}=\frac{b-c}{a}$
$\Rightarrow a^{2}b+a^{2}c=b^{2}c-{bc}^2$
$\Rightarrow a^2(b+c)=bc(b+c)$ ..... ( cancelling $(b+c)$ on both sides)
$\Rightarrow a^2=bc$
$\Rightarrow a=\sqrt{bc}$