Question

two integers differ by 12 and the sum of their squares is 74. find the integers
two integers differ by 12 and the sum of their squares is 74. find the integers
@Mathematics

Answer 1

Let the integers be x and y.
x-y=12
x=y+12
x^2+y^2=74
(y+12)^2+y^2=74
y^2+24y+144+y^2=74
2y^2+24y+144-74=0
2y^2+24y+70=0
y^2+12y+35=0
y^2+7y+5y+35=0
y(y+7)+5(y+7)=0
(y+7)(y+5)=0
y+7=0 or y+5=0
y=-7 or y=-5
plug in the values of y in x-y=12 to find x. There will be two values