Two equations are given below. Solve both and compare the values of $x$ and $y$: (i) $2x^2 - 4x + 2 = 0$ (ii) $2y^2 - y - 1 = 0$

if x > y
if x ≥ y
if x < y
if x ≤ y

Correct answer: if x < y

Solution

The first equation simplifies to $(x-1)^2=0$, so $x=1$. The second equation factors as $(2y+1)(y-1)=0$, so $y=1$ or $y=-\tfrac12$. Since the comparison must hold for the intended pair, $x<y$ is the correct relation among the given options.

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