If - - - are the roots of x2-k-1x-1-2k2-k-1-0- then show that - 2- 2-k-

α ^2+β ^2=(α +β )^2 2αβ =(k+1)^2 2×1/2(k^2+k+1) since α +β = b/a=k+1; #160; #160; #160;αβ =c/a=1/2(k^2+k+1) =k^2+2k+1 k^2 k 1 ∴α ...

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Integration by Partial Fractions

If α , β ar...

Question

If $α, β$ are the roots of $x^{2} - (k + 1) x + \frac{1}{2} (k^{2} + k + 1) = 0,$ then show that $α^{2} + β^{2} = k .$

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