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InterviewSolution
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Let a,b,c be positive real numbers in H.P. Statement -1: `(a+b)/(2a-b)+(c+b)/(2c-b)ge4` Statement-2: `(a)/(b)+(b)/(c)+(c)/(a)ge3`A. Statement -1 is true, Statement -2 is True, Statement -2 is a correct explanation for Statement for Statement -1.B. Statement -1 is true, Statement -2 is True, Statement -2 is not a correct explanation for Statement for Statement -1.C. Statement -1 is true, Statement -2 is False.D. Statement -1 is False, Statement -2 is True. |
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Answer» Correct Answer - B Since a,b,c are in H.P. Therefore, `b=(2ac)/(a+c)`. Now, `(a+b)/(2a-b)+(c+b)/(2c-b)=(a+(2ac)/(a+c))/(2a-(2ac)/(a+c))+(c+(2ac)/(a+c))/(2c-(2ac)/(a+c))` `=(1+3c)/(2a)+(c+3a)/(2c)` `=(1)/(2)+(3c)/(2a)+(1)/(2)+(3a)/(2c)` `=1+(3)/(2)((1)/(c)+(c)/(a))` `ge1+3=4" "[AMgtGM,(a)/(c)+(c)/(a)ge2]` So, statement-1 is true. Using `AMgeGm`, we obtain `(a^(2)c+b^(2)a+c^(2)b)/(3)ge(a^(2)cxxb^(2)axxc^(2)b)^(1//3)` `rArr" "a^(2)c+b^(2)a+c^(2)bge3abcrArr(a)/(b)+(b)/(c)+(c)/(a)ge3` So, statement -2 is true. But, statement -2 is not a correct explanation for statement -1. |
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