已知XY=5,(X-Y)²=16,求:(1)X²+Y² (2)X+Y
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已知XY=5,(X-Y)²=16,求:(1)X²+Y² (2)X+Y
x^2+y^2=(x-y)²+2xy=16+10=26
(x+y)^2=(x-y)²+4xy=16+20=36
所以x+y=6,-6
16=(X-Y)²=X²-2XY+Y²,又XY=5,故 X²+Y² =26
(X+Y)²=X²+2XY+Y²=36,故X+Y=+ - 6
x^2+y^2=(x-y)²+2xy=16+10=26
(x+y)^2=(x-y)²+4xy=16+20=36
所以x+y=6,-6