Question

Two numbers differ by 3. The sum of their reciprocals is 7 / 10. Find the numbers

Answer 1

let two number be x and y
x-y=3 equation1
1/x+1/y=7/10 equation2
but y=x+3
substitute in equation2
we get 7x^2+x+30
solving the quadratic equation
x=2 or -15/7
when x=2
then y=5
when x=-15/7
then y=6/7
therefore
x=2 y=5