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Question

If x=2+3,xy=1, then find x2-x+y2-y.


A

3

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B

3

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C

2

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D

2

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Solution

The correct option is D

-2


Finding x2-x+y2-y

Given that x=2+3,xy=1

x2-x+y2-y

=x2-x+y2-y=x2-x+xy2x-1(xy=1y=1x)=x2-x+12x-1=2+32-(2+3)+12(2+3)-1=2+32-2-3+12×2+23-1=2+3-3+13+23=-6-73-6+333+23(addingboththefraction)=-12+6333+23=-12+6333+6=-6(2+3)3(2+3)=-63=-2

Hence, the correct answer is (D)-2


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