QJEEM22Mac87d: JEE Main 2022 Mathematics - Class 11 JEEM22Mac87d Solution: Let p and q be two real numbers such that p + q = 3 and p 4 + q …

$\because$ $p + q = 3$ ...... (i)

and ${p^4} + {q^4} = 369$ ...... (ii)

${\{ {(p + q)^2} - 2pq\} ^2} - 2{p^2}{q^2} = 369$

or ${(9 - 2pq)^2} - 2{(pq)^2} = 369$

or ${(pq)^2} - 18pq - 144 = 0$

$\therefore$ $pq = - 6$ or 24

But $pq = 24$ is not possible

$\therefore$ $pq = - 6$

Hence, ${\left( {{1 \over p} + {1 \over q}} \right)^{ - 2}} = {\left( {{{pq} \over {p + q}}} \right)^2} = {( - 2)^2} = 4$