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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 + β2 + 2αβ = 36 ⇒ α2 + β2 = 36 – 2 x 6 = 24 Now, α3 + β3 + α2 + β2 + α + β = (α + β) (α2 + β2 - αβ) + (α2 + β2 ) + (α + β ) = 6(24 – 6) + 24 + 6 = 6 × 18 + 30 = 138. |
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