SOLUTION: two numbers differ by 2. The sum. of their squares is 244.find the numbers

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
---------------------------------------
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

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

two numbers differ by 2. The sum. of their squares is 244.find the numbers

RELATED QUESTIONS
Two number differ by 2 the sum of their squares is 244 find the... (answered by mananth)
two numbers differ by 7 and the sum of their squares is 29. find the numbers (answered by JBarnum,Stitch)
The sum of two numbers is 22, and the sum of their squares is 244. Find the... (answered by ewatrrr)
two numbers differ by 9. the sum of their squares is 653. what are the... (answered by josgarithmetic)
two numbers differ by 8 and the sum of their squares is 320. find the two... (answered by drk)
Two positive numbers differ by 5 and the squares of their sum is 169. Find the... (answered by sofiyac)
two positive numbers differ by 7 and the sum of their squares is 169. find the numbers. (answered by Tatiana_Stebko)
Two numbers differ by 7,the different of their squares is 91,find the... (answered by ankor@dixie-net.com)
Two positive numbers differ by 6, and their squares differ by 96. Find the... (answered by ankor@dixie-net.com)