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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Badiuddin

 

The equation is equivalent to (x-y)²+(x-4)²+(y-4)² = 0 which means x=y=4 is the only solution.