若正数x,y满足x-y=5,xy=11/4,则x+y=_____

若正数x,y满足x-y=5,xy=11/4,则x+y=_____
若正数x,y满足x-y=5,xy=11/4,则x+y=_____

若正数x,y满足x-y=5,xy=11/4,则x+y=_____
(x-y)²=5²
x²-2xy+y²=25
x²+y²=25+2xy=25+11/2=61/2
(x+y)²
=x²+2xy+y²
=51/2+11/2
=31
所以x+y=-√31或√31

x-y=5
(x-y)^2=x^2-2xy+y^2=25 xy=11/4
x^2+y^2=61/2
(x+y)^2=x^2+2xy+y^2=61/2+11/2=36
x+y=6

这题出错了吧

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