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If x = 1/(√11 + √10) and

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by Brent@GMATPrepNow » Wed Mar 01, 2017 8:04 am
If x = 1/(√11 + √10) and y = 1/(√11 - √10), then what is the value of x² - xy + y²?

A) 39
B) 41
C) 43
D) 45
E) 47

Answer: B

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by regor60 » Wed Mar 01, 2017 10:40 am
x^2-xy+y^2 = (x-y)^2+xy

x-y = (11^1/2 - 10^1/2 -11^1/2 -10^1/2)/11-10 = -2*10^1/2

xy = 1/(11^1/2+10^1/2)*(11^1/2-10^1/2) = 1/(11-10)= 1

(-2*10^1/2)^2 + 1 = 4*10 + 1= B
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by Matt@VeritasPrep » Wed Mar 01, 2017 2:32 pm
x² - xy + y² = (x - y)² + xy

x - y is easy enough to find: -2√10. From there, plug in:

(-2√10)² + 1/(√11 + √10) * 1/(√11 - √10) =>

40 + 1/(11 - 10) =>

41
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