Two operators are defined by p q=(p2+q2)/(pq) and p q=p2/q. If x y=22, then x=

GATE 2021 CE (CE1) – Question 4

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

Two operators are defined by $p\oplus q=(p^2+q^2)/(pq)$ and $p\odot q=p^2/q$. If $x\oplus y=2\odot2$, then $x=$

$y/2$
$y$
$3y/2$
$2y$

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Show answer and explanation

Correct answer: (B) $y$

Explanation

The right side is $2^2/2=2$. Hence $x^2+y^2=2xy$, or $(x-y)^2=0$. Since the operator requires nonzero denominators, the valid solution is **x=y (B)**.