JEE Main 2022 · 26 Jun · Shift 2 · Mathematics Q22

MathematicsInteger+4 / -1Question 22 of 90

Let $p$ and $q$ be two real numbers such that $p+q=3$ and $p^4+q^4=369$ . Then $\left(\dfrac1p+\dfrac1q\right)^{-2}$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 4

Let $s=pq$ . $p^4+q^4=(9-2s)^2-2s^2=81-36s+2s^2=369$ , so $s^2-18s-144=0$ : $s=24$ or $-6$ .

Real roots need $9-4s\ge0$ , so $s=-6$ .

Value. $\left(\dfrac{p+q}{pq}\right)^{-2}=\left(\dfrac s3\right)^2=4$ .

Answer: 4

JEE Main 2022 · 26 Jun · Shift 2, Mathematics question 22