Question

若x-2/x=5,则x^2+4/x^2=________

若x=1984，y=1916时，计算（x^4-y^4)/(x^2-2xy+y^2)*(y-x)/(x^2+y^2)=_______
若2x=-y,则(xy)/(x^2-y^2)=_______

Answer 1

1.
若x-2/x=5
两边平方得x²-4+4/x²=25
所以x²+4/x²=29
2.
若x=1984，y=1916时
(x⁴-y⁴)/(x²-2xy+y²)*(y-x)/(x²+y²)
=(x²+y²)(x²-y²)(y-x)/(x-y)²(x²+y²)
=(x²-y²)(y-x)/(x-y)²
=(x+y)(x-y)(y-x)/(x-y)²
=-(x+y)
=-(1984+1916)
=-3900
3.
若2x=-y
那么y=-2x
所以(xy)/(x²-y²)
=x*(-2x)/[x²-(-2x)²]
=-2x²/(-3x²)
=2/3

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Answer 2

1.x-2/x=5
(x-2/x)^2
x^2-4+4/x^2=25
x^2+4/x^2=4+25=29
2.（x^4-y^4)/(x^2-2xy+y^2)*(y-x)/(x^2+y^2)=
=(x^2+y^2)(x+y)/(x-y)*(y-x)/(x^2+y^2)
=-(x+y)
=-(1984+1916)
=-3900
3.2x=-y
(xy)/(x^2-y^2)
=-2x^2/(-3x^2)
=2/3

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