Question

If `alphaa n dbeta` are the roots of `x^2-a(x-1)+b=0` then find the value of `1//(alpha^2-aalpha)+1//(beta^2-beta)+2//a+bdot`

Answer 1

Correct Answer - Zero
Let `alpha, beta ` be the roots of the equation ` x^(2) - a (x - 1) + b = 0` . Then
` alpha^(2) a alpha + a + b = 0 and beta^(2) - a beta + a + b = 0`
`therefore alpha ^(2) - a alpha = beta^(2) - abeta = - a- b`
`rArr (1)/(a^(2) - alpha ) + (1)/(beta^(2) - a beta) + (2)/(a + b ) = 0` .