Use the Binomial Theorem to write in the form for some positive integers and .

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Use the Binomial Theorem to write $(3+\sqrt{5})^4$ in the form $a + b\sqrt{5}$ for some positive integers $a$ and $b$ .

Mellie May 7, 2015

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Best Answer

+129852

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(3 + √5)^4 =

3^4 + 4*(3)^3(√5) + 6(3)^2*5 + 4*(3)(√5)^3 + (√5)^4 =

81 + 108√5 + 270 + 12*5√5 + 25 =

81 + 108√5 + 270 + 60√5 + 25 =

376 + 168√5

Not too much to that, huh ???

CPhill May 7, 2015

1⁺⁰ Answers

+129852

+10

Best Answer

(3 + √5)^4 =

3^4 + 4*(3)^3(√5) + 6(3)^2*5 + 4*(3)(√5)^3 + (√5)^4 =

81 + 108√5 + 270 + 12*5√5 + 25 =

81 + 108√5 + 270 + 60√5 + 25 =

376 + 168√5

Not too much to that, huh ???

CPhill May 7, 2015

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