If - - Y are such that - y -2- -2-2- Y 2-6- -3-3- y 3-8- then -4-4- Y 4 is equal to-A- none of theseB- 12C- 10D- 18

The correct option is D 18(α + β + γ)^2 = α^2 + β^2+γ^2 + 2(αβ + βγ + γα) 4 = 6 + 2(αβ + βγ + γα) ⇒αβ + βγ + γα = 1 Also, α^3 + β^3+γ^3 3 αβγ =(α + β + γ)( ...

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Quantitative Aptitude

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If α, β, Y ar...

Question

If $α, β, γ$ are such that $α + β + γ = 2$ , $α^{2} + β^{2} + γ^{2} = 6, α^{3} + β^{3} + γ^{3} = 8$ , then $α^{4} + β^{4} + γ^{4}$ is equal to:

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none of these

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Solution

The correct option is C 18
$(α + β + γ)^{2} = α^{2} + β^{2} + γ^{2} + 2 (α β + β γ + γ α)$
$4 = 6 + 2 (α β + β γ + γ α)$
$\Rightarrow α β + β γ + γ α = - 1$
Also, $α^{3} + β^{3} + γ^{3} - 3 α β γ$
$= (α + β + γ) (α^{2} + β^{2} + γ^{2} - α β - β γ - γ α)$
$8 - (3 α β γ) = 2 (6 + 1)$
$\Rightarrow α β γ = - 2$
Now, $(α^{2} + β^{2} + γ^{2})^{2} = \sum α^{4} + 2 \sum β^{2} γ^{2}$
$= \sum α^{4} + 2 [(\sum β γ)^{2} - 2 α β γ (\sum γ)]$
$\Rightarrow \sum α^{4} = 36 - 2 [(- 1)^{3} - 2 (- 2) (2)] = 18$

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If α, β, γ are such that α+β+γ=2, α2+β2+γ2=6, α3+β3+γ3=8, then α4+β4+γ4 is equal to:

If $α, β, γ$ are such that $α + β + γ = 2$ , $α^{2} + β^{2} + γ^{2} = 6, α^{3} + β^{3} + γ^{3} = 8$ , then $α^{4} + β^{4} + γ^{4}$ is equal to: