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sudarshan gupta Grade: Upto college level
        

the number of number pairs (x,y) which will satisfy the equation x2-xy+y2=4(x+y-4)

7 years ago

Answers : (3)

nikhil tilak
8 Points
										

by applying delta =0 condition we see that the above represents a pair of lines.so infinite points satisfy the equation.

7 years ago
Badiuddin askIITians.ismu Expert
147 Points
										

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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7 years ago
mycroft holmes
269 Points
										

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

7 years ago
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