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If x+y = 30 and x^3+y^3=8100, what's the value of x^2+y^2?

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If x+y = 30 and x^3+y^3=8100, what's the value of x^2+y^2?  [#permalink]

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New post 08 Apr 2019, 14:42
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Difficulty:

  65% (hard)

Question Stats:

53% (02:24) correct 47% (03:08) wrong based on 36 sessions

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If \(x + y = 30\) and \(x^3 + y^3=8100\), what is the value of \(x^2+y^2\)?

A. \(480\)
B. \((15 + \sqrt{15})^2\)
C. \(420\)
D. \(880\)
E. Information is not sufficient to answer

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Re: If x+y = 30 and x^3+y^3=8100, what's the value of x^2+y^2?  [#permalink]

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New post 08 Apr 2019, 19:05
(x+y)^3= x^3 + y^3 + 3xy(x+y)
hence xy= 210
(x+y)2=x^2+y^2 -2xy
x^2+y^2=480
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If x+y = 30 and x^3+y^3=8100, what's the value of x^2+y^2?  [#permalink]

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New post 09 Apr 2019, 17:17
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\(x + y = 30\)
\(x^3 + y^3 = 8100\)
\(x^2 + y^2 = ?\)

\((x + y)^2 = x^2 + 2xy + y^2 = 900\)

\(x^2 + y^2 = 900 -2xy\)

and

\((x^2 + y^2)(x + y) = x^3 + x^2y + xy^2 + y^3\)

\((x^2 + y^2)(x + y) = (x^3 + y^3) + xy(x+y)\)

So combining both

\((900 - 2xy)(30) = (8100) + xy(30)\)

\(27,000 - 60xy = 8100 + 30xy\)

\(xy = 210\)

\(x^2 + y^2 = 900 -2(210)\)

\(x^2 + y^2 =480\)

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If x+y = 30 and x^3+y^3=8100, what's the value of x^2+y^2?   [#permalink] 09 Apr 2019, 17:17
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