For positive reals x,y and positive integers m,n: xⁿy^m (1+x²ⁿ)(1+y^2m) > 14.

JEE PYQ

[JEE Advanced 1989] for positive reals x y and positive integers m n x ny m 1

VAVidaara Admin Asked 2d ago 0 views 1 answer

For positive reals $x,y$ and positive integers $m,n$: $\dfrac{x^ny^m}{(1+x^{2n})(1+y^{2m})}>\dfrac14$.

VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 2d ago ▲ 0

Answer: False.

$1+x^{2n}\ge2x^n$ and $1+y^{2m}\ge2y^m$, so the expression is $\le\frac14$ — never strictly greater.

JEE Advanced 1989 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.

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