If - - - are the roots of x3-x2-1-0- then the value of 1-1-1-1-1-1-y is equal to-

The correct option is A 5 Roots of x^3 x^2 1=0 are α, β, γ Let y = 1+x/1 x⇒ x = y 1/y+1. Then (y 1)^3/(y+1)^3 ( y 1/y+1 )^2 1 = 0 i.e., (y 1)^3 (y 1)^2( ...

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Standard XII

Mathematics

Range

If α, β, γ ar...

Question

If $α, β, γ$ are the roots of $x^{3} - x^{2} - 1$ = 0, then the value of $\frac{1 + α}{1 - α} + \frac{1 + β}{1 - β} + \frac{1 + γ}{1 - γ}$ is equal to:

-5

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Solution

The correct option is A
-5

Roots of $x^{3} - x^{2} - 1 = 0$ are $α, β, γ$

Let y = $\frac{1 + x}{1 - x} \Rightarrow x$ = $\frac{y - 1}{y + 1}$ . Then

$\frac{(y - 1)^{3}}{(y + 1)^{3}}$ - ${(\frac{y - 1}{y + 1})}^{2} - 1 = 0$

i.e., $(y - 1)^{3} - (y - 1)^{2} (y + 1) - (y + 1)^{3} = 0$

i.e., $y^{3} + 5 y^{2} - y + 1 = 0$ has roots

$\frac{1 + α}{1 - α}$ , $\frac{1 + β}{1 - β}$ , $\frac{1 + γ}{1 - γ}$ , whose sum = -5

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Similar questions

Q. If

α, β, γ

are roots of

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the value of

\frac{1 + α}{1 - α} + \frac{1 + β}{1 - β} + \frac{1 + γ}{1 - γ} =

Q. If

α, β, γ

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(α + β)^{- 1} + (β + γ)^{- 1} + (γ + α)^{- 1} =

If α, β, γ are the roots of the equation $x^{3} + 4 x + 1 = 0$ ,then $(α + β)^{- 1} + (β + γ)^{- 1} + (γ + α)^{- 1} =$

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If α,β,γ are the roots of x3−x2−1 = 0, then the value of 1+α1−α+1+β1−β+1+γ1−γ is equal to:

The correct option is A -5 Roots of x3−x2−1=0 are α,β,γ Let y = 1+x1−x⇒x = y−1y+1. Then (y−1)3(y+1)3 - (y−1y+1)2−1=0 i.e., (y−1)3−(y−1)2(y+1)−(y+1)3=0 i.e., y3+5y2−y+1=0 has roots 1+α1−α,1+β1−β,1+γ1−γ, whose sum = -5

If $α, β, γ$ are the roots of $x^{3} - x^{2} - 1$ = 0, then the value of $\frac{1 + α}{1 - α} + \frac{1 + β}{1 - β} + \frac{1 + γ}{1 - γ}$ is equal to: