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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
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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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19 Sep 2019, 07:16
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65% (01:21) correct 
