InterviewSolution
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InterviewSolution
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If `alpha and beta` be the roots of the equation `x^(2) + px - 1//(2p^(2)) = 0`, where `p in R`. Then the minimum value of `alpha^(4) + beta^(4)` isA. `2sqrt2`B. `2 - sqrt2`C. `2`D. `2 + sqrt2` |
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Answer» Correct Answer - 4 Here, `alpha^(4) + beta^(4) = (alpha^(2) + beta^(2))^(2) - 2alpha^(2)beta^(2)` `= {(alpha + beta)^(2) - 2alphabeta}^(2) - 2(alphabeta)^(2)` `= (p^(2) + 1/p^(2))^(2) - (1)/(2p^(4))` `= p^(4) + (1)/(2p^(4)) + 2` `= (p^(2) - (1)/(sqrt2 p^(2)))^(2) + 2 + sqrt2 ge 2 + sqrt2` Thus, the minimum value of `alpha^(4) + beta^(4)` is `2 + sqrt2`. |
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