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Question

If x2+xy+x=12 and y2+xy+y=18, then the value of x+y is __________?

A
5 or 6
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B
3 or 4
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C
5 or 3
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D
6 or 3
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Solution

The correct option is A 5 or 6
Let x2+xy+x=12 ...(i)
and y2+xy+y=18 ...(ii)
Adding (i) and (ii), we get
(x2+y2+2xy)+x+y=30
(x+y)2+(x+y)30=0
Let (x+y)=t
Thus t2+t30=0
t2+(65)t30=0
t2+6t5t30=0
t(t+6)5(t+6)=0
(t+6)(t5)=0
which gives t=6or t=5
So, t=x+y=6 or 5
Hence, option A is correct.

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