x+y=a+b and ax-by=a×a+b×b . Find the value of x and y.
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x+y=a+b and ax-by=a^2+b^2
now
(a+b)^2=a^2+b^2+2ab
(x+y)^2=ax-by+2ab
x^2+y^2+2xy=ax-by+2ab
x^2-ax+y^2+by+2xy-2ab=0
x (x-a)+y (y+b)+2 (xy-ab)=0
now sum of any numbers is zero then the numbers are individually equal to zero
so.
x (x-a)=0 and y (y+b)=0
now solving above
x=a and y= -b
that's all...
now
(a+b)^2=a^2+b^2+2ab
(x+y)^2=ax-by+2ab
x^2+y^2+2xy=ax-by+2ab
x^2-ax+y^2+by+2xy-2ab=0
x (x-a)+y (y+b)+2 (xy-ab)=0
now sum of any numbers is zero then the numbers are individually equal to zero
so.
x (x-a)=0 and y (y+b)=0
now solving above
x=a and y= -b
that's all...
Tauqueer11:
a×a= a square
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