Question

Let p and q be two real numbers such that p + q = 3 and p⁴ + q⁴ = 369. Then
\((\frac{1}{p} + \frac{1}{q} )^{-2}\)
is equal to _______.

Answer 1

Correct Answer: 4

The correct answer is 4
∵ p + q = 3 …(i)
and p⁴ + q⁴ = 369 …(ii)
{(p + q)² – 2pq}² – 2p²q² = 369
or (9 – 2pq)² – 2(pq)² = 369
or (pq)² – 18pq – 144 = 0
∴ pq = –6 or 24
But pq = 24 is not possible
∴ pq = –6
Therefore 
\((\frac{1}{p} + \frac{1}{q} )^{-2}\)
 \(= ( \frac{pq}{p+q})\)
\( = ( -2)² = 4\)