1.

If α and β are the roots of the equation x2 – 6x + 6 = 0, what is α3 + β3 + α2 + β2 + α + β equal to ?(a) 150 (b) 138 (c) 128 (d) 124

Answer»

(b) 138.

α + β = 6, αβ = 6

(α + β)2 = 62 ⇒ α2 + β+ 2αβ = 36 

⇒ α2 + β2 = 36 – 2 x 6 = 24 

Now, α3 + β3 + α2 + β2 + α + β 

= (α + β) (α2 + β- αβ) + (α2 + β2 ) + (α + β ) 

= 6(24 – 6) + 24 + 6 = 6 × 18 + 30 = 138.



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