Question

If p/q = r/s = t/u = √5, then what is the value of [(3p2 + 4r2 + 5t2)/(3q2 + 4s2 + 5u2)]?

Answer 1

p = sqrt of 5 ×q
r = sqrt of 5 × s
t = sqrt of 5 × u
putting it in the numerator the answer comes to be 5

Answer 2

Answer:

5

Step-by-step explanation:

If $\frac{p}{q}=\frac{r}{s}=\frac{t}{u}=\sqrt{5}$, then

$p=\sqrt{5}q$, $r=\sqrt{5}s$ and $t=\sqrt{5}u$

Now, the given expression is:

$\frac{3p^{2}+4r^{2}+5t^{2}}{3q^{2}+4s^{2}+5u^{2}}$

Substituting the values of p,r and t in the above expression, we get

=$\frac{3(5q^{2})+4(5s^{2})+5(5u^{2})}{3q^{2}+4s^{2}+5u^{2}}$

=$\frac{15q^{2}+20s^{2}+25u^{2}}{3q^{2}+4s^{2}+5u^{2}}$

=$\frac{5(3q^{2}+4s^{2}+5u^{2})}{3q^{2}+4s^{2}+5u^{2}}$

=$5(1)$

=$5$