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Ganesh Garg
Asked: 2022-11-03T07:22:08+05:30 In:

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 1
B. Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1
C. Statement 1 is true, Statement 2 is false
D. Statement 1 is false, Statement 2 is true

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 1
B. Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation 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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  1. 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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