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the number of number pairs (x,y) which will satisfy the equation x 2 -xy+y 2 =4(x+y-4)

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

Grade:Upto college level

3 Answers

nikhil tilak
8 Points
11 years ago

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

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

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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mycroft holmes
272 Points
11 years ago

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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