Question

let alpha eta are roots of x2-x-1=0 then alpha^5+beta^5

Answer 1

Answer:

Step-by-step explanation:

[math]ax^2+bx+c=0[/math]

[math]\alpha +\beta=\frac{-b}{a}[/math]

[math]\alpha*\beta=\frac{c}{a}[/math]

[math]\alpha+\frac{1}{\beta}=\frac{\alpha*\beta+1}{\beta}[/math]

[math]\beta+\frac{1}{\alpha}=\frac{\alpha*\beta+1}{\alpha}[/math]

Sum of Roots[math]:[/math]

[math]\frac{\alpha\beta+1}{\beta}+\frac{\alpha\beta+1}{\alpha}[/math]

[math]=\frac{\beta[\alpha\beta+1]+\alpha[\alpha\beta+1]}{\alpha\beta}[/math]

[math]=\frac{(\alpha+\beta)(\alpha\beta +1)}{\alpha\beta}[/math]

[math]=\frac{-b/a(c/a+1)}{c/a}[/math]

Hope it helps you

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