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the number of number pairs (x,y) which will satisfy the equation x2-xy+y2=4(x+y-4)
by applying delta =0 condition we see that the above represents a pair of lines.so infinite points satisfy the equation.
Dear sudarshan
x2-xy+y2=4(x+y-4)
x2-x(y+4)+y2 -4y +16=0
if it has real solution then D≥0
so (y+4)2 -4( y2 -4y +16)≥0
or (y-4)2 ≤0
only possible when y=4
so for y=4 only one value of x=4 possible
so only one pair (4,4) is the solution
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The equation is equivalent to (x-y)2+(x-4)2+(y-4)2 = 0 which means x=y=4 is the only solution.
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