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

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