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Question

Number of real ordered pair (x,y) satisfying x2+1=y and y2+1=x is

A
0
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B
1
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C
2
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D
4
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Solution

The correct option is A 0
x2+1=y and y2+1=x
Subtracting x2y2=yx
(xy)(x+y+1)=0
x=y or x+y+1=0
If x=y then x2+1=yx2x+1=0 which has no real roots.
If x+y+1=0 then x+y=1
Adding given equations, x2+y2+2=x+y
x2+y2+2=1x2+y2+3=0 which is not possible.

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