已知X+Y=7①XY=2②求2X²+2Y²；2（X²-Y²)的解!

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已知X+Y=7①XY=2②求2X²+2Y²；2（X²-Y²)的解!
已知X+Y=7①XY=2②求2X²+2Y²；2（X²-Y²)的解!

已知X+Y=7①XY=2②求2X²+2Y²；2（X²-Y²)的解!
1、
(x+y)²=7²
x²+y²+2xy=49
x²+y²=49-2xy=45
所以2x²+2y²=90
2、
(x-y)²
=x²+y²-2xy
=41
x-y=±√41
所以2(x²-y²)
=2(x+y)(x-y)
=±14√41

2X²+2Y²=90
2（X²-Y²)=14倍根号82

2X^2+2Y^2=2(X+Y)^2-4XY=90
2（X2-Y2)=2*[(X2-Y2)^2]^(1/2)=2[(X^2+Y^2)^2-4(xy)^2]^(1/2)=7799/87

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