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Given I. $x^{2} = 36$
II. $y^{2} - 13 y + 42 = 0$ , which relation between $x$ and $y$ is true?

Competition practiceQuadratic Comparison

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

Step-by-Step Solution

I:

x = 6

or −6. II:

(y - 6) (y - 7) = 0

, so

y = 6

or 7. Both values of

x

are at most 6, and the smallest

y

is 6, so

x

≤

y

.

Answer: C)

x

≤

y

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