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What is the relation between $x$ and $y$ if I. $x^{2} = 81$
II. $y^{2} - 20 y + 99 = 0$ ?

Competition practiceQuadratic Comparison

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

Step-by-Step Solution

I.

x = 9

or −9. II.

(y - 9) (y - 11) = 0

, so

y = 9

or 11. The largest

x

(9) equals the smallest

y

(9), so

x

≤

y

.

Answer: A)

x

≤

y

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