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If x + y = 10 and xy = 4, then what is the value of x4 + y4?
- A8464
- B8432
- C7478
- D6218
Answer not set
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CCommunity
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
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