Question

12. If x2 + y2 - xy = 3 and y - x = 1, then
ху
x² + y²​

Answer 1

We have y−x=1 or y=1+x

Substitute y=1+x in the equation we get

x

2

+y

2

−xy=3

⇒x

2

+(1+x)

2

−x(1+x)=3

⇒x

2

+x

2

+2x+1−x−x

2

−3=0

⇒x

2

+x−2=0

⇒(x−1)(x+2)=0

∴x=1,−2

When x=1⇒y=1+x=1+1=2

When x=−2⇒y=1+x=1−2=−1

∴{1,2} and {−2,−1} are the solutions of the above equations.