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Let $x$ = (√3 + √2)/(√3 − √2) and $y$ = (√3 − √2)/(√3 + √2). Find $x^{2} + x y + y^{2}$ .

Competition practiceAlgebra

A99
B97
C100
D98

Step-by-Step Solution

x = 5 + 2

√6 and

y = 5 - 2

√6, so

x + y = 10

and

x y = 1

. Then

x^{2} + x y + y^{2} = (x + y)^{2} - x y = 100 - 1 = 99

.

Answer: A) 99

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