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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)

8 years ago

Answers : (3)

nikhil tilak
8 Points

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

8 years ago
Badiuddin askIITians.ismu Expert
147 Points

Dear sudarshan


  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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8 years ago
mycroft holmes
271 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.

8 years ago
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