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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

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
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
Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE  & AIEEE preparation. All the best. Regards,Askiitians ExpertsBadiuddin

```
7 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.
```
7 years ago
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