CAT 2018 Slot 1 — QA Question 28

Let X and Y are the two real numbers.

X × Y × 73 − X × Y × 37 = 720

X × Y × (73 – 37) = 720

X × Y × 36 = 720

X × Y = 20

AM(X², Y²) ≥ GM(X², Y²)

∴ $\frac{X^2+Y^2}{2}$ ≥ $\sqrt{X^2\times Y^2}$

∴ (X² + Y²) ≥ 40

Alternately, 
We know, X × Y = 40

Also, (X - Y)² ≥ 0 [Square of any number is always greater than or equal to zero]

∴ X² + Y² - 2XY ≥ 0

∴ X² + Y² ≥ 2XY

∴ X² + Y² ≥ 40

Hence, 40.