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  • x2+y2-xy=3andy-x=1 then find xy/x2+y2

x2+y2-xy=3andy-x=1 then find xy/x2+y2

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We have y-x=1 , or, y=1+x
Substituting y=1+x,in the equation we get
x^2+y^2-xy=3
Rightarrow x^2+(1+x)^2-x(1+x)=3
Rightarrow x^2+x^2+2x+1-x-x^2-3=0
Rightarrow x^2+x-2=0
Rightarrow (x-1)(x+2)=0
herefore x=1,-2
When x=1Rightarrow y=2
When x=-2Rightarrow y=-1
herefore (1,2) , and, (-2,-1) are the solutions of the above equation

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Deependra Verma

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