Question

find the value of x 10 - 5(1+ x) /3 + (3x +1) /5 = 0​

Answer 1

Answer:

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If (x+1/x) = 6, what is the value of (X^5+1/x^5)?

Let x=cosθ+isinθ

1x=cosθ−isinθ

x+1x=2cosθ=6 (given)

cosθ=3 ; This is impossible but still it works.

x5=(cosθ+ isinθ)5=cos5θ+isin5θ

x5+1x5=2cos5θ

But cos5θ=16cos5θ−20cos3θ+5cosθ

x5+1x5=2(16∗35–20∗33+5∗3)

=6726

x+1/x=6 ……………..(1)

Squaring both sides

x^2+1/x^2+2=36

x^2+1/x^2=34 ………..(2)

On cubing eq.(1) both sides

x^3+1/x^3+3.x1/x.(x+1/x)=216

x^3+1/x^3+3×6=216

x^3+1/x^3=216–18

x^3+1/x^3=198………………(3)

Multiply eq.(2) & (3)

(x^2+1/x^2)×(x^3+1/x^3)=34×198

x^5+x+1/x+1/x^5=6732

x^5+6+1/x^5=6732

x^5+1/x^5=6732–6=6726.