Question

If $\frac{p}{q}=\frac{r}{s}=\frac{t}{u}=\sqrt{6}$, then what is the value of $\frac{4p^2+5r^2+6t^2}{4q^2+5s^2+6u^2}$?

• A. $\sqrt{6}$
• B. 6
• C. 3
• D. $\frac{1}{6}$
• E. None of the above

Answer 1

The correct option is B 6

$\frac{p}{q}=\frac{r}{s}=\frac{t}{u}=\sqrt{6}$ $\Rightarrow$ p = q$\sqrt{6}$, r = s$\sqrt{6}$, t = u$\sqrt{6}$

So, $\frac{4p^2+5r^2+6t^2}{4q^2+5s^2+6u^2}$ = $\frac{24p^2+30s^2+36u^2}{4q^2+5s^2+6u^2}$ = 6