如果x1,x2是一元二次方程ax²+bx+c=0的两根,那么有x1+x2=-b/a,x1x2=c/a.接上面,已知x1,x2是方程x²-4x+2=0的两根,求:(1)(x1-x2)²的值;(2)x1²-x2²的值
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![如果x1,x2是一元二次方程ax²+bx+c=0的两根,那么有x1+x2=-b/a,x1x2=c/a.接上面,已知x1,x2是方程x²-4x+2=0的两根,求:(1)(x1-x2)²的值;(2)x1²-x2²的值](/uploads/image/z/1598932-28-2.jpg?t=%E5%A6%82%E6%9E%9Cx1%2Cx2%E6%98%AF%E4%B8%80%E5%85%83%E4%BA%8C%E6%AC%A1%E6%96%B9%E7%A8%8Bax%26%23178%3B%2Bbx%2Bc%3D0%E7%9A%84%E4%B8%A4%E6%A0%B9%2C%E9%82%A3%E4%B9%88%E6%9C%89x1%2Bx2%3D-b%2Fa%2Cx1x2%3Dc%2Fa.%E6%8E%A5%E4%B8%8A%E9%9D%A2%2C%E5%B7%B2%E7%9F%A5x1%2Cx2%E6%98%AF%E6%96%B9%E7%A8%8Bx%26%23178%3B-4x%2B2%3D0%E7%9A%84%E4%B8%A4%E6%A0%B9%2C%E6%B1%82%EF%BC%9A%281%29%28x1-x2%29%26%23178%3B%E7%9A%84%E5%80%BC%3B%282%29x1%26%23178%3B-x2%26%23178%3B%E7%9A%84%E5%80%BC)
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如果x1,x2是一元二次方程ax²+bx+c=0的两根,那么有x1+x2=-b/a,x1x2=c/a.接上面,已知x1,x2是方程x²-4x+2=0的两根,求:(1)(x1-x2)²的值;(2)x1²-x2²的值
如果x1,x2是一元二次方程ax²+bx+c=0的两根,那么有x1+x2=-b/a,x1x2=c/a.
接上面,已知x1,x2是方程x²-4x+2=0的两根,求:(1)(x1-x2)²的值;(2)x1²-x2²的值
如果x1,x2是一元二次方程ax²+bx+c=0的两根,那么有x1+x2=-b/a,x1x2=c/a.接上面,已知x1,x2是方程x²-4x+2=0的两根,求:(1)(x1-x2)²的值;(2)x1²-x2²的值
(x1-x2)²=(x1+x2)²-4x1x2=16-8=8
x1²-x2²=(x1+x2)²-2x1x2=16-4=12
(x1-x2)²=(-b/a)²-4c/a
x1²-x2²=(-b/a)²-2c/a
x1+x2=4
x1x2=2
所以(x1-x2)²=(x1+x2)²-4x1x2=16-8=8
x1²-x2²=(x1+x2)²-2x1x2=16-4=12