SOLUTION: In solving the problem below, use a variable/s to represent the unknown quantity or quantities. Formulate the equation that will solve the problem. Solve the equation and check if

Question 912722: In solving the problem below, use a variable/s to represent the unknown quantity or quantities. Formulate the equation that will solve the problem. Solve the equation and check if your solution is valid. Thank you!
Find two numbers whose sum is 12 and the sum whose squares is 74.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let numbers be x & y
x+y =12
x^2+y^2=74
x^2+y^2= (x+y)^2-2xy
x+y=12
x^2+y^2= 74 = 12^2-2xy
74=144-2xy
2xy=70
xy=35
y=35/x
x+y=12
x+35/x= 12
x^2+35=12x
x^2-12x+35=0
x^2-7x-5x+35=0
x(x-7)-5(x-7)=0
(x-7)(x-5)=0
x=7 OR 5
when x= 7 y=5
when x =5 y=7
CHECK
7^2+5^2= 49+25 = 74
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