If b is the mean proportional of a and c then the mean proportional of a2 + b2 and b2 + c2 is ______.

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KollegeApply · Accepted Answer

If b is the mean proportional of a and c then the mean proportional of a2 + b2 and b2 + c2 is ab + bc. Explanation: Let x be the mean proportional between a2 + b2 and b2 + c2 Then, a2 + b2 : x : : x : b2 + c2 `(a^2 + b^2)/x = x/(b^2 + c^2)` x2 = (a2 + b2) (b2 + c2) x2 = a2b2 + a2c2 + b4 + b2c2 Given b is the mean proportional of a and c b2 = ac Substitute: x2 = a2(ac) + a2c2 + (ac)2 + (ac)c2 x2 = a3c + 2a2c2 + ac3 x2 = ac(a2 + 2ac + c2) x2 = ac(a + c)2 x = sqrt(ac) (a + c) x = b(a + c) x = ab + bc

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