X1,X2是两个不相等的实数,且满足X1²-2009X1=1,X2²-2009X2=1,那么X1X2=?如果x1、x2是两个不相等的实数,且满足x1的平方减去2009倍的x1等于1,x2的平方减去2009倍的x2等于1,那么x1与x2的乘积等于多少?
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![X1,X2是两个不相等的实数,且满足X1²-2009X1=1,X2²-2009X2=1,那么X1X2=?如果x1、x2是两个不相等的实数,且满足x1的平方减去2009倍的x1等于1,x2的平方减去2009倍的x2等于1,那么x1与x2的乘积等于多少?](/uploads/image/z/8577659-11-9.jpg?t=X1%2CX2%E6%98%AF%E4%B8%A4%E4%B8%AA%E4%B8%8D%E7%9B%B8%E7%AD%89%E7%9A%84%E5%AE%9E%E6%95%B0%2C%E4%B8%94%E6%BB%A1%E8%B6%B3X1%26sup2%3B-2009X1%3D1%2CX2%26sup2%3B-2009X2%3D1%2C%E9%82%A3%E4%B9%88X1X2%3D%3F%E5%A6%82%E6%9E%9Cx1%E3%80%81x2%E6%98%AF%E4%B8%A4%E4%B8%AA%E4%B8%8D%E7%9B%B8%E7%AD%89%E7%9A%84%E5%AE%9E%E6%95%B0%2C%E4%B8%94%E6%BB%A1%E8%B6%B3x1%E7%9A%84%E5%B9%B3%E6%96%B9%E5%87%8F%E5%8E%BB2009%E5%80%8D%E7%9A%84x1%E7%AD%89%E4%BA%8E1%2Cx2%E7%9A%84%E5%B9%B3%E6%96%B9%E5%87%8F%E5%8E%BB2009%E5%80%8D%E7%9A%84x2%E7%AD%89%E4%BA%8E1%2C%E9%82%A3%E4%B9%88x1%E4%B8%8Ex2%E7%9A%84%E4%B9%98%E7%A7%AF%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F)
X1,X2是两个不相等的实数,且满足X1²-2009X1=1,X2²-2009X2=1,那么X1X2=?如果x1、x2是两个不相等的实数,且满足x1的平方减去2009倍的x1等于1,x2的平方减去2009倍的x2等于1,那么x1与x2的乘积等于多少?
X1,X2是两个不相等的实数,且满足X1²-2009X1=1,X2²-2009X2=1,那么X1X2=?
如果x1、x2是两个不相等的实数,且满足x1的平方减去2009倍的x1等于1,x2的平方减去2009倍的x2等于1,那么x1与x2的乘积等于多少?
X1,X2是两个不相等的实数,且满足X1²-2009X1=1,X2²-2009X2=1,那么X1X2=?如果x1、x2是两个不相等的实数,且满足x1的平方减去2009倍的x1等于1,x2的平方减去2009倍的x2等于1,那么x1与x2的乘积等于多少?
两式做差:
(X1²-X2²)-2009*(X1-X2)=0
所以(X1-X2)(X1+X2-2009)=0
因为x1不等于x2,
所以X1+X2=2009
X1²-2009X1=X1*(X1-2009)=X1*(-X2)=1
所以X1*X2=-1
X1²-2009X1=1 1
X2²-2009X2=1 2
1式减2式得
x1^2-2009x1-x2^2+2009x2=0
(x1+x2)(x1-x2)-2009(x1-x2)=0
(x1-x2)(x1+x2-2009)=0
∵x1<>x2
∴x1+x2-2009=0
x1+x2=...
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X1²-2009X1=1 1
X2²-2009X2=1 2
1式减2式得
x1^2-2009x1-x2^2+2009x2=0
(x1+x2)(x1-x2)-2009(x1-x2)=0
(x1-x2)(x1+x2-2009)=0
∵x1<>x2
∴x1+x2-2009=0
x1+x2=2009 平方一下得
x1^2+2x1x2+x2^2=2009^2 3
1式+2式得
x1^2+x2^2-2009(x1+x2)=2
x1^2+x2^2-2009*2009=2
x1^2+x2^2=2009^2+2 4
4式代入3式得
2009^2+2+2x1x2=2009^2
x1x2=-1
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