Question 1055985: two numbers differ by 2. The sum. of their squares is 244.find the numbers Found 2 solutions by addingup, MathTherapy:Answer by addingup(3677) (Show Source):
You can put this solution on YOUR website! x = y-2
x^2+y^2 = 244 substitute for x:
(y-2)^2+y^2 = 244
(y-2)(y-2)+y^2 = 244
2y^2-4y+4 = 244 Divide both sides by 2:
y^2-2y+2 = 122 Complete the squares
y^2-2y = 120 take 1/2 the coefficient of y and add to both sides. The coefficient is 2, 1/2 of 2 is 1:
y^2-2y+1 = 121
(y-1)^2 = 121 Take the square root on both sides:
y-1 = -11 or y-1 = 11
y = -10 or y = 12
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We are not looking for a negative number, so let's try 12:
x = y-2
x = 12-2 = 10
The sum of their squares is 244:
12^2+10^2 = 244
244 = 244 Correct
:
John
