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If A1 and A2 be the two .Ms between two ...

If `A_1` and `A_2` be the two .Ms between two numbers 7 and 1/7 then `(2A_1-A_2)(2A_2-A_1)=`

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If A_1 and A_2 are two A.M.’s between a and b, prove that : (2A_1-A_2)(2A_2-A_1) =ab .

If one geometric mean G and two arithmetic means A_1 and A_2 be inserted between two given quantities, prove that : G^2=(2A_1-A_2)(2A_2-A_1) .

Knowledge Check

  • If A_1,A_2 be two AM's and G_1,G_2 be the two GM's between two number a and b , then (A_1+A_2)/(G_1G_2) is equal to

    A
    `(a+b)/(2ab)`
    B
    `(2ab)/(a+b)`
    C
    `(a+b)/(ab)`
    D
    `(ab)/(a+b)`

  • If A_1 and A_2 are two AMs between a and b then (2A_1 -A_2) (2A_2 - A_1) =

    A
    `(a)/(b)`
    B
    ` (b)/(a)`
    C
    `ba `
    D
    ` a^(2)b`

    • Similar Questions

    Explore conceptually related problems

    If A_1 and A_2 are two A.M.s between a and b and G_1 and G_2 are two G.M.s between the same numbers then what is the value of (A_1+A_2)/(G_1G_2)

    If A_1,A_2 be two A.M.\'s G_1,G_2 be the two G.M.\'s and H_1,H_2 be the two H.M.\'s between a and b then (A) (A_1+A_2)/(G_1 G_2)=(a+b)/(ab) (B) (H_1+H_2)/(H_1 H_2)=(a+b)/(ab) (C) (G_1G_2)/(H_1 H_2)=(A_1+A_2)/(H_1+H_2) (D) (A_1+A_2)(H_1+H_2)/(H_1 H_2)=(a+b)/(a-b)

    If A_1,A_2 be two A.M.\'s G_1,G_2 be the two G.M.\'s and H_1,H_2 be the two H.M.\'s between a and b then (A) (A_1+A_2)/(G_1 G_2)=(a+b)/ab (B) (H_1+H_2)/(H_1 H_2)=(a+b)/ab (C) (G_1G_2)/(H_1 H_2)=(A_1+A_2)/(H_1+H_2) (D) (A_1+A_2)/(H_1 H_2)=(a+b)/(a-b)

    If A_1,A_2 be two A.M.\'s G_1,G_2 be the two G.M.\'s and H_1,H_2 be the two H.M.\'s between a and b then (A) (A_1+A_2)/(G_1 G_2)=(a+b)/(ab) (B) (H_1+H_2)/(H_1 H_2)=(a+b)/ab (C) (G_1G_2)/(H_1 H_2)=(A_1+A_2)/(H_1+H_2) (D) (A_1+A_2)/(H_1 H_2)=(a+b)/(a-b)

    If A_1,A_2,G_1,G_2 and H_1,H_2 are AM’s, GM’s and HM’s between two numbers, then (A_1+A_2)/(H_1+H_2). (H_1H_2)/(G_1G_2) equals _____

    If A_1,A_2,G_1,G_2 and H_1,H_2 are AM’s, GM’s and HM’s between two numbers, then (A_1+A_2)/(H_1+H_2). (H_1H_2)/(G_1G_2) equals _____

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