Question
The AM of two positive numbers a & b exceeds their GM by 3/2 & the GM exceeds the HM by 6/5 such that a+b= α , |a-b|=β , then which of them are correct,
1) α + β² = 96 2) α + β² =74 3)α²+β = 234 4)α²+β = 84
(a+b)/2 = √ab + 3/2 (1) or a+b = 2√ab + 3
√ab = 2ab/(a+b) + 6/5 (2) or 5(a+b)√ab = 10ab + 6(a+b)
on solving these 2 we get 5[2√ab + 3]√ab = 10ab + 6[2√ab + 3]
or 10ab + 15√ab = 10ab + 12√ab + 18
or 3√ab = 18 or ab = 36 and a+b = 15 = α
so a-b = √(225 - 144) = √81 = 9 = β