The ratio of the A.M. and G.M. of two positive numbers a and b, is m : n. Show that
a : b = (m +(m2 – n2)
1/2) : (m -(m2 – n2)
1/2).
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Positive number a,b
A.M=2a+b GM=ab
m:n=2aba+b
R.H.S=(m−m2−n2)(m+m2−n2)
Divide by n in both numerator and denominator.
=(nm−n2m2−1)(nm+n2m2−1)
=(2aba+b−4aba2+b2+2ab
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