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What is the relation between $x$ and $y$ when $x^{2} - 21 x + 110 = 0$ and $y^{2} - 15 y + 54 = 0$ ?

Competition practiceQuadratic Comparison

A $x$ ≤ $y$
B $x$ ≥ $y$
C $x > y$
D $x < y$

Step-by-Step Solution

x^{2} - 21 x + 110 = (x - 10) (x - 11)

, so

x = 10

or 11.

y^{2} - 15 y + 54 = (y - 6) (y - 9)

, so

y = 6

or 9. Every

x

exceeds every

y

, so

x > y

.

Answer: C)

x > y

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