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If `a, b, c` are in `G.P.` and `b-c, c-a, a-b` are in `H.P.` then find the value of `((a+b+c)^(2))/(b^(2))` . |
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Answer» Correct Answer - 9 If `a, b, c` are in …….. `a, b, c rarr G.P` `implies b^(2)=ac`. `b-c, c-a, a-b rarr H.P.` `implies (2)/(c-a)=(1)/(b-c)+(1)/(a-b)` `(2)/(c-a) = (a-c)/((b-c)xx(a-b))` `implies 2(ab-ac-b^(2)+bc)= - (a-c)^(2)` `2ab+2bc-2ac-2b^(2)= -a^(2)-c^(2)+2ac` `a^(2)+b^(2)+c^(2)+2ab+2bc+2ca=6ac+3b^(2)=9ac` `(a+b+c)^(2) = 9ac` `((a+b+c)^(2))/(b^(2))=9` |
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