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Question

If x2+y2+1x2+1y2=4, then the value of x2+y2 is

A
2
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B
4
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C
8
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D
16
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Solution

The correct option is A 2
Since the question contains variables, we can assume any value for x and y.
Let, x = y = 1. Then,
x2+y2+1x2+1y2=1+1+1+1=4=4, which is true as per given equation.
x2+y2=1+1=2.
Hence, option (a) is correct answer.

Alternatively:
x2+y2+1x2+1y24=0x2+1x22+y2+1y22=0(x1x)2+(y1y)2=0x1x=0x21=0x=1,1Similary,y=1,1x2+y2=1+1=2

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