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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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Manager
Joined: 21 Feb 2019
Posts: 112
Location: Italy
If x+y = 30 and x^3+y^3=8100, what's the value of x^2+y^2?  [#permalink]

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08 Apr 2019, 14:42
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Difficulty:

65% (hard)

Question Stats:

50% (02:19) correct 50% (02:59) wrong based on 30 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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MEMENTO AUDERE SEMPER
Manager
Joined: 07 Apr 2018
Posts: 89
Location: United States
Concentration: General Management, Marketing
GPA: 3.8
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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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
Manager
Joined: 12 Sep 2017
Posts: 223
If x+y = 30 and x^3+y^3=8100, what's the value of x^2+y^2?  [#permalink]

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09 Apr 2019, 17:17
1
$$x + y = 30$$
$$x^3 + y^3 = 8100$$
$$x^2 + y^2 = ?$$

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

$$x^2 + y^2 = 900 -2xy$$

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

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

$$27,000 - 60xy = 8100 + 30xy$$

$$xy = 210$$

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

$$x^2 + y^2 =480$$

A
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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