若x+y=4,xy=3,求y/x + x/y的值.

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若x+y=4,xy=3,求y/x+x/y的值.若x+y=4,xy=3,求y/x+x/y的值.若x+y=4,xy=3,求y/x+x/y的值.y/x+x/y=y²/(xy)+x²/(x

若x+y=4,xy=3,求y/x + x/y的值.
若x+y=4,xy=3,求y/x + x/y的值.

若x+y=4,xy=3,求y/x + x/y的值.
y/x + x/y
=y²/(xy)+x²/(xy)
=(x²+y²)/(xy)
=(x²+y²+2xy)/(xy)-2
=(x+y)²/(xy)-2
=4²/3-2
=10/3

y/x + x/y
=(x^2+y^2)/xy
=(x+y)^2/xy-2
=16/3 -2
=10/3

若x+y=4,xy=3,求y/x + x/y的值

y/x+x/y
=(x+y)/xy
=4/3
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10/3


y/x+x/y
=(x²+y²)/xy
=[(x+y)²-2xy]/xy
=[4²-2*3]/3
=(16-6)/3
=10/3

.x=1,y=3或者y=1,x=3,答案都为10/3
服了那些 这种题也能做错的大虾们

x=4-y→(4-y)y=3 →y^2-4y+3=0→(y-1)(y-3)=0→y=1或3 →x=3或1→y/x + x/y=10/3


y/x + x/y=(x^2+y^2)/xy=(x^2+y^2)/3
由x+y=4 (1),
xy=3 (2)
(1)式两边平方减2*(2)=(x+y)^2-2xy=x^2+y^2=16-6=10
所以y/x + x/y=(x^2+y^2)/xy=(x^2+y^2)/3=10/3

求得x^2+y^2=(x+y)^2-2xy=10
所以原式=(x^2+y^2)/xy=10/3

y/x + x/y=y²/(xy)+x²/(xy)
=(x²+y²)/(xy)
=(x²+y²+2xy)/(xy)-2
=(x+y)²/(xy)-2
=16/3-2
=10/3