InterviewSolution
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InterviewSolution
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Statement -1: If a,b,c are distinct real numbers in H.P, then `a^(n)+c^(n)gt2b^(n)" for all "ninN`. Statement -2: `AMgtGMgtHM` |
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Answer» `therefore GgtH` `therefore sqrt(ac)gtb` `implies (ac)^((n)/(2))gtb^(n) " or " a^((n)/(2))c^((n)/(2))gtb^(n) " " "....(i)"` Also, `(a^((n)/(2))-c^((n)/(2)))^(2)gt0 implies a^(n)+c^(n)-2a^((n)/(2))c^((n)/(2))gt0` `implies a^(n)+c^(n)gt2a^((n)/(2))c^((n)/(2))gt2b^(n)" " [" from Eq.(i) "]"....(i)"` `therefore a^(n)+c^(n)gt2b^(n)` |
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