Question

If $\log \frac{(x+y)}{4}=\log \sqrt{x}+\log \sqrt{y}$ prove that $(x^2+y^2)=14xy$.

Answer 1

Given,

$\log \frac{(x+y)}{4}=\log \sqrt{x}+\log \sqrt{y}$

or, $\log \frac{x+y}{4}=\log \sqrt{xy}$

or, $\frac{x+y}{4}=\sqrt{xy}$

or, $(x+y{)}^2=16xy$ [ Squaring both sides we get]

or, $x^2+y^2=14xy$.