InterviewSolution
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InterviewSolution
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If A, G & H are respectively the A.M., G.M. & H.M. of three positive numbers a, b, & c, then equation whose roots are a, b, & c is given by |
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Answer» `A = (a+b+c)/3` `a+b+c = 3A `eqn(1) `G= (abc)^(1/3)` `abc = G^3` `H= 3/((1/a) + (1/b) + (1/c))` `H= 3/((bc+ab+ca)/(abc)) = (3abc)/(b+bc+ ca)` `ab+bc+ca = (3abc)/H = (3G^3)/H` eqn(3) `x^3 - (a+b+c)x^2 + (ab+bc+ca)x - (abc) = 0` `x^3 - 3Ax^2 +(3G^3/H)x - G^3 = 0` `x^3 - 3Ax^2 +(3G^3/H)x - G^3 = 0` answer |
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