Question

A.M. of two numbers is $50$ and H.M. is $18$. Find the numbers.

Answer 1

Let $a,b$ be two numbers.

$A.M.=50\frac{a+b}{2}=50=>a+b=100H.M.=18\frac{2}{\frac{1}{a}+\frac{1}{b}}=182ab=1800=>ab=900{(a+b)}^2-4ab={(a-b)}^2=6400a-b=80b=10,a=90$

$90,10$ are two numbers.