Two numbers differ by 7, and the sum of their squares is 29. Find the numbers.

let numbers are x and y. then x-y=7...............(1) and x^2+y^2=29 From (1), \left(x-y\right)^2=49 x^2+y^2-2xy=49 29-2xy=49 xy=-10 then y=-10/x, Now from (1), x+\frac{10}{x}=7 x^2-7x+10=0 so x=2,5, then y=-5,-2 So the numbers are 2,-5 or 5,-2