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Consider a equation `x^(3)-3x=sqrt(x+2)` such that `x` is a real number then sum of its positive roots is `lamda` where `[(lamda)/2]` is______ |
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Answer» Correct Answer - 1 If `xgt2` then `x^(3)-3xge4x-x=xge sqrt(x+2)` `implies|x|le2` take `x=2costheta` for some `theta epsilon[0,pi]` `implies2cos3theta=sqrt(2(1+costheta))` `implies2"sin"(7theta)/4."sin"(5theta)/4=0` `impliestheta=0, (4pi)7, (4pi)/5` `:. X-2, 2"cos"(4pi)/7, -1.2(1+sqrt(5))` |
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