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Statement 1 If a and b be two positive numbers, where `agtb` and `4xxGM=5xxHM` for the numbers. Then, `a=4b`. Statement 2 `(AM)(HM)=(GM)^(2)` is true for positive numbers.A. Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1B. Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1C. Statement 1 is true, Statement 2 is falseD. Statement 1 is false, Statement 2 is true |
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Answer» Correct Answer - C `:.A=(a+b)/(2),G=sqrt(ab) " and " H=(2ab)/(a+b)` Given, `4G=5H" " "……(i)"` and `G^(2)=AH` `:. H=(G^(2)))/(A)" " "……(ii)"` From Eqs. (i) and (ii), we get `4G=(5G^(2))/(A) implies 4A=5G` `implies 2(a+b)=5sqrt(ab)` `implies4(a^(2)+b^(2)+2ab)=25ab` `implies 4a^(2)-17ab+4b^(2)=0` `implies (a-4b)(4a-b)=0` `a=4b,4a-b ne 0" " [:.agtb]` `:.` Statement 1 is true. Statement 2 is true only for two numbers, if numbers more than two, then this formula`(AM)(HM)=(GM)^(2)` is true, if numbers are in GP. Statement 2 is false for positive numbers. |
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