AM between two numbers whose sum is 100 is ti the GM as ``5:4`, find the numbers.

Explanation

Let the numbers be a and b.
Then, `a+b=100`
or `2A=100`
`implies A=50 " " "……(i)"`
and given, `(A)/(G)=(5)/(4) implies (50)/(G)=(5)/(4) " " [ " from Eq. (i) "]`
`therefore G=40 " " "…….(ii)"`
From important theorem `a,b=A pm sqrt((A+G)(A-G))`
`=50 pm sqrt((50+40)(50-40))`
`=50 pm 30=80,20`
`therefore a=80,b=20`
or `a=20, b=80`