If the sum of two numbers is 17 and the sum of their square is 145 - what is the larger number?

Answer 1

This information gives us the equations: x + y = 17 x2 + y2 = 145 These equations are more difficult to solve. The solution to the equations is below. Possibly easier (at least with this specific question) is guessing and checking. The answers are 8 and 9. To check: 8 + 9 = 17 64 + 81 = 145 === === The equations we have are: x + y = 17 x2 + y2 = 145 Lets substitue by using the first equation: x = -y + 17 plug that in: (-y + 17)2 + y2 = 145 Now simplify: y2 - 34y + 289 + y2 = 145 Simplify a little more: 2y2 - 34y + 289 = 145 Create a quadratic equation: 2y2 - 34y + 144 = 0 Factor the polynomial (or use the quadratic formula): (y - 9)(2y - 16) = 0 So either: y - 9 = 0 so y = 9, Or 2y - 16 = 0 so y = 8. Note: Because both equations are symmetric (meaning x and y can be switched without changing anything, like x + y = 17 is the same as y + x = 17), we know that x and y are each either 8 or 9. Either way the answers are 8 and 9. Plug these into the original equations and they work. Otherwise, just plug the y values into the easiest equation to solve for x. So x + 8 = 17 so x = 9. The other option is x + 9 = 17 which leads to x = 8. The answers are (8,9) and (9,8). Either way, the two numbers to fill the requirements are 8 and 9.