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24 vote

If x + y = 10 and xy = 4, then what is the value of x4 + y4?

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If x + y = 10 and xy = 4, then what is the value of x4 + y4?
1). 8464
2). 8432
3). 7478
4). 6218


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1 answers

37 vote
Answered by on | Votes 37 |

Using algebraic identities,

x2 + y2 + 2xy = (x + y)2

⇒ x2 + y2 = (x + y)2 - 2xy

⇒ x2 + y2 = (10)2 - 2 × 4 [? x + y = 10 and xy = 4}

⇒ x2 + y2 = 92

Squaring on both side,

⇒ (x2+ y2)2 = 922

⇒ x4 + y4 + 2x2y2 = 8464

⇒ x4 + y4 = 8464 - 2(xy)2

⇒ x4 + y4 = 8464 - 2(4)2 [? xy = 4]

∴ x4 + y4 = 8432
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