Question

The sum of two numbers is17 and the sum of their squares is 145. Find the larger number.

Answer 1

The larger number is 9. One way to get this is to take two numbers that add up to 17, in this case your numbers are 8 and 9. Multiply 8 by 8 which will result in 64. Next you want to multiply 9 by 9 which is 81. If you add 81 and 64 you get 145. The final step is to simply pick the larger number between 8 and 9, which is 9.

Answer 2

Let the two numbers be x and y

x^2 + y^2 = 145

x + y = 17 Solve for y

y = 17 - x

x^2 + (17 - x)^2 = 145

x^2 + 289 - 34x + x^2 = 145

2x^2 - 34x + 289 = 145 Subtract 145 from both sides.

2x^2 -34x + 289 - 145 = 0

2x^2 - 34x + 144 = 0

x^2 - 17x + 72 = 0

(x - 9)(x - 8) = 0

x = 9 or x = 8

y = 9 or y = 8

The larger number is 9

I did it because I wanted to show if anything else would show up. If you haven't taken any algebra, ignore this answer.