CAT Exam Model Paper 7 with solutions for free online practice

Question : 15 of 60

Marks: +1, -0

What is the number of non-negative integer solutions for the equation

x^{2}-x y+y^{2}=x+y ?

3
4
1
None of these

Validate

Solution:

x^{2}-x y+y^{2}=x+y

Multiplying both sides by 2:

2 (x^{2}-x y+y^{2} )=2(x+y)

(x-y)^{2}+x^{2}+y^{2}=2 x+2 y

\table (x-y)^{2},+,(x-1)^{2},+,(y-1)^{2},=,2 ;↓,,↓,,↓,,;0,,1,,1,→, (\A);1,,0,,1,→,(\B);1,,1,,0,→,(\C)

Integer solutions for (x, y):
Case 1: (0, 0)and (2,2)
Case 2: (1,2) and (1,0)
Case 3: (2 ,1)and (0,1)
So there are six non-negative integer solutions.

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