The difference of two numbers is 3 and the sum of their squares is 65. find the numbers
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let two numbers be x and y
a/q x-y=3
x=3+y
and x^2+y^2=65
(3+y)^2+y^2=65
9+y^2+6y+y^2=65
2y^2+6y-56=0
2y^2+14y-8y-56=0
2y(y+7)-8(y+7)=0
(2y-8)(y+7)=0
then y=4,-7
if y=4 ,x=7
and y=-7,x=-4
a/q x-y=3
x=3+y
and x^2+y^2=65
(3+y)^2+y^2=65
9+y^2+6y+y^2=65
2y^2+6y-56=0
2y^2+14y-8y-56=0
2y(y+7)-8(y+7)=0
(2y-8)(y+7)=0
then y=4,-7
if y=4 ,x=7
and y=-7,x=-4
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