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Prove that the Quadratic equation whose roots are a and b is given by x2-2Ax+G2=0 where A =Arithmetic mean   and G is the geometric mean of a and b respectively.

Asked by Topperlearning User 5th October 2016, 7:16 AM
Answered by Expert

the quadratic equation with roots a and b is given by x2-(a+b)x+ab=0

the arithmetic mean of a and b is A=(a+b)/2rightwards double arrowa+b=2A

The geometric mean of a and b is G=square root of a b end root rightwards double arrow G squared equals a b

So the equation becomes x2-2Ax+G2=0

Answered by Expert 5th October 2016, 9:16 AM
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