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If α, β are the roots of x2 - 2x + 2 = 0 then the equation whose roots are α4, β4
1. x2 - 8x + 16 = 0
2. x2 + 8x + 16 = 0
3. x2 - 8x - 16 = 0
4. x2 + 8x - 16 = 0

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Correct Answer - Option 2 : x2 + 8x + 16 = 0

Calculation:

α, β are the roots of x- 2x + 2 = 0 

Then, α + β = 2 , αβ = 2 

⇒ (α + β)2 = 22

⇒ α2 + β2 + 2αβ = 4

⇒ α2 + β= 4 - 4 = 0

⇒ (α2 + β)2 = 0

⇒ α4 + β4 + 2α2β2 = 0

⇒ α4 + β4 = - 8 

⇒ α4β4 = 24 = 16 

The equation whose roots are α4, β4

⇒  x2 - (α4 + β4 )x + α4β4 = 0

⇒ x2 + 8x + 16 = 0

∴ The equation whose roots are α4, β4 is x2 + 8x + 16 = 0.

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