InterviewSolution
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InterviewSolution
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Let `a`is a real number satisfying `a^3+1/(a^3)=18`. Then the value of `a^4+1/(a^4)-39`is ____. |
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Answer» Correct Answer - `a^(4) + (1)/(a^(4)) = 47` Let ` a + (1)/(a) = t` `therefore t^(3) - 3t - 18 = 0` t - 3 satisfies this equation `therefore (t - 3 ) (t^(2) _ 3t + 6 ) = 0` Clearly, t = 3 is the only soultion `therefore a ^(2) + (1)/(a) = 3` `rArr a^(2) + (1)/(a^(2)) = 7` `rArr a^(4) + (1)/(a^(4)) = 47` . |
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