If alpha and beta are the roots of x² = x + 1 then the value of alpha²/beta - beta²/alpha
Answers
Answered by
34
Answer:
x^2 = x + 1
=> x^2 - x - 1 = 0
As it is given that the roots of this equation are α, β, we can, by the use of the sum and product of roots formulae, say that,
α + β = -(-1)/1 = 1
αβ = -1
Now, we are asked to find the value of
α^2/β - β^2/α.
= (α^3 - β^3) / αβ
= (α - β)(α^2 + αβ + β^2) / -1
= -√[(α + β)^2 - 4αβ] [(α + β)^2 - αβ]
= -√[1 - 4(-1)] (1 - (-1))
= -2√5
Answered by
24
Answer:
-2√5
Step-by-step explanation:
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