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)
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