已知x+y=1,xy=1/5,求 （x^2+1)(y^2+1)

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已知x+y=1,xy=1/5,求 （x^2+1)(y^2+1)
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已知x+y=1,xy=1/5,求 （x^2+1)(y^2+1)
已知x+y=1,xy=1/5,求 （x^2+1)(y^2+1)

已知x+y=1,xy=1/5,求 （x^2+1)(y^2+1)
（x^2+1)(y^2+1)
=x²y²+x²+y²+1
=x²y²-2xy+1+x²+y²+2xy
=(xy-1)²+(x+y)²
=(1/5-1)²+1²
=16/25+1
=41/25

（x^2+1)(y^2+1)
=x^2y^2+x^2+y^2+1
=(xy)^2+(x+y)^2-2xy+1
=(xy)^2-2xy+1+(x+y)^2
=(xy-1)^2+(x+y)^2
=(1/5-1)^2+1^2
=16/25+1
=41/25

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