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Re: If xy = 7 and x – y = 7, then x² +
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22 Mar 2017, 14:43

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Top Contributor

1

GMATPrepNow wrote:

If xy = 7 and x – y = 7, then x² + y² =

(A) 35 (B) 42 (C) 49 (D) 56 (E) 63

The important thing to recognize here is that if we square (x - y), we get a x² term and a y² term. We also get an extra xy term, but that's okay, because we're given some information about the product xy.

So, take: x – y = 7 and... Square both sides: (x - y)² = 7² Expand: x² - 2xy + y² = 49 Since we're told xy = 7, we'll replace xy with 7 to get: x² - 2(7) + y² = 49 Simplify: x² - 14 + y² = 49 Add 14 to both sides: x² + y² = 63

“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.” ― Henry Wadsworth Longfellow

Re: If xy = 7 and x – y = 7, then x² +
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16 Jul 2017, 13:09

If xy = 7 and x – y = 7, then x² + y² =

\((x - y)^2 = x^2 - 2xy + y^2\)

\(x^2 + y^2 = (x - y)^2 + 2xy\)

\(x^2 + y^2 = (7)^2 + 2 * 7\)

\(x^2 + y^2 = 49 + 14\)

\(x^2 + y^2 = 63\)

Hence, Answer is E

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Re: If xy = 7 and x – y = 7, then x² +
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23 Aug 2018, 11:44

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