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Question 19
If $$\sqrt{(1 - p^2)(1 - q^2)} = \frac{\sqrt{3}}{2}$$, then what is the value of $$\sqrt{2p^2 + 2q^2 + 2pq} + \sqrt{2p^2 + 2q^2 - 2pq}$$?
Solution
From $$\sqrt{(1-p^2)(1-q^2)}=\frac{\sqrt{3}}{2}\ $$
we can say that :
$$(1-p^2)(1-q^2)=\frac{3}{4}=\left(1-0^2\right)\left(1-\frac{1}{2^2}\right)\ .$$
So, either p/q=0/(1/2) .
So,Â
$$\sqrt{2p^2+2q^2+2pq}+\sqrt{2p^2+2q^2-2pq}=\sqrt{\ 0+2\times\frac{1}{4}+0}+\sqrt{0+2\times\frac{1}{4}-0}=\sqrt{\frac{1}{2}}+\sqrt{\frac{1}{2}}=\frac{2}{\sqrt{2}}=\sqrt{2}.$$
So, B is correct choice.
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