Question

If the AM of two positive numbers a and b be twice their GM, show that a:b=(2+√3):(2-√3)

Answer 1

Answer:

let three no a, b, c and their AM =A and GM=G

then we know that x=A+/-√(A^2-G^2) where x is the numbers and given

A=2G put this value into the above equation.we get a=(2+√3)/2 and b=(2-√3)/2

so a:b=(2+√3):(2-√3)