Question

1.If a and B are the roots of x^2 = x + 1 then value of alpha^2/beta - beta^2/alpha
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Answer 1

HEY MATE,

We are given the equation

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

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Hope it helps....Brainliest Pls...