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Let A;G;H be the arithmetic; geometric a...

Let A;G;H be the arithmetic; geometric and harmonic means between three given no. a;b;c then the equation having a;b;c as its root is

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The correct Answer is:
`x^3-3Ax^2+3G^3/H x-G^3=0`
We have
`A = (a + b + c)/(3) implies a + b + c = 34`
`G (abc)^(1//3) implies abc = G^(3)`
`(1)/(H) = ((1)/(a) + (1)/(b) + (1)/(c ))/(3) = (ab + bc + ca)/(3abc)`
`implies (3G^(3))/(H) = ab + bc + ca`
The equation having a, b and c as its roots is
`x^(3) - (a + b+ c) x^(2) + (ab + bc + ca) x - abc = 0`
or `x^(3) - 3Ax^(2) + (3G^(3))/(H) x - G^(3) = 0`
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