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Question

Solve the system of equations ⎪ ⎪ ⎪⎪ ⎪ ⎪1x+1y=321x2+1y2=54

A
(1,2)
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B
(1,3)
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C
(2,3)
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D
(2,2)
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Solution

The correct option is A (1,2)
1x+1y=32,1x2+1y2=54,1x=a,1y=b,a+b=32,a2+b2=54,(a+b)2=(32)2=a2+b2+2ab=94,54+2ab=94,2ab=1,b=12a,a+12a=32,2a2+1=3a,2a22aa+1=0,(2a1)(a1)=0,a=12or1,b=12or1,xandy=1and2

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