SOLUTION: find two numbers whose sum is 13 and the difference of their squares is 39

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Question 925217: find two numbers whose sum is 13 and the difference of their squares is 39
Answer by srinivas.g(540) About Me  (Show Source):
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let numbers be x, y
so x%2By=+13
+x%5E2-y%5E2+=39
Formulae: +a%5E2-b%5E2+=+%28a%2Bb%29%2A%28a-b%29
+%28x%2By%29%2A%28x-y%29+=39
put x+y= 13 in above equation
+13%2A%28x-y%29+=39
divide with 13 on both sides
+13%2A%28x-y%29%2F13+=39%2F13
x-y=+3
but x+y= 13 adding above equations
x-y= 3
x+y= 13
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2x = 16
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2x=16
divide with 2 on both sides
+2x%2F2+=+16%2F2
x=8
put x= 8 in x-y =3
8-y =3
move -y to the right
8=y+3
move 3 to the left
8-3 = y
5= y
so y= 5
result : x=8 , y=5