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
Source: GMAT Prep Now
Difficulty level: 650 - 700
If x = 1/(√11 + √10) and
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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
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