two numbers add up to 144. one number is half the square of the other number. what are the numbers

Answer 1

x+y = 144

x = y^2/2

(1/2)y^2 + y = 144

y^2 +2y = 288

complete the square

y^2 +2y + 1 = 288+1

(y+1)^2 = 289

y +1 = + or - sqr289

y = -1 + or - 17

y = -18 or 16

x = 144-16 = 128 or 144+18= 162

(x,y) = (128,16) or (162,-18)

either solution sums to 144

x=y^2/2 = 256/2 = 128

or

= -18^2/2 = 324/2 = 162