InterviewSolution
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InterviewSolution
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If `alpha, beta` are the roots of the equation `x^(2) - lm + m = 0`, then find the value of `1/(alpha^(2)) + 1/(beta^(2))` in terms of l and m. |
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Answer» Given, `alpha, beta` are the roots of `x^(2) - lx + m = 0` `rArr` Sum of the roots `= alpha + beta = (-(-l))/(1) = L " "(1)` `rArr` Product of the roots `= alpha beta = (m)/(1) = m" "(2)` Now, `1/(alpha^(2)) + 1/(beta^(2)) = (alpha^(2) + beta^(2))/(alpha^(2)beta^(2))` `= ((alpha^(2) + beta^(2))^(2) - 2(alphabeta))/((alphabeta)^(2))` Substituting the values of `alpha + beta` and `alphabeta` in the above equation , we get , `(1)/(alpha^(2)) +(1)/(beta^(2)) = (l^(2)-2m)/(m^(2))` `:.` The value of `1/(alpha^(2)) + 1/(beta^(2)) = (l^(2) - 2m)/(m^(2))`. |
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