Question 89

If $$\frac{p}{q}=\frac{r}{s}=\frac{t}{u}=\sqrt{5}$$, then what is the value of $$[\frac{(3p^{2} + 4r^{2} + 5t^{2})}{(3q^{2} + 4s^{2} + 5u^{2})}]$$ ?

Solution

Given : $$\frac{p}{q}=\frac{r}{s}=\frac{t}{u}=\sqrt{5}$$

=> $$p=\sqrt5q$$ , $$r=\sqrt5s$$ , $$t=\sqrt5u$$

To find : $$[\frac{(3p^{2} + 4r^{2} + 5t^{2})}{(3q^{2} + 4s^{2} + 5u^{2})}]$$

= $$\frac{3(\sqrt5q)^2+4(\sqrt5s)^2+5(\sqrt5u)^2}{3q^2+4s^2+5u^2}$$

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

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

=> Ans - (B)

Share on Whatsapp Share on Whatsapp

Create a FREE account and get: