一元二次方程ax²+bx+c=0(a≠0)的两根为x₁和x₂.求:(1)|x₁-x₂|和(x₁+x₂)/2(2)x₁的三次方+x₂的三次方
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![一元二次方程ax²+bx+c=0(a≠0)的两根为x₁和x₂.求:(1)|x₁-x₂|和(x₁+x₂)/2(2)x₁的三次方+x₂的三次方](/uploads/image/z/1786029-69-9.jpg?t=%E4%B8%80%E5%85%83%E4%BA%8C%E6%AC%A1%E6%96%B9%E7%A8%8Bax%26%23178%3B%2Bbx%2Bc%3D0%EF%BC%88a%E2%89%A00%EF%BC%89%E7%9A%84%E4%B8%A4%E6%A0%B9%E4%B8%BAx%26%238321%3B%E5%92%8Cx%26%238322%3B.%E6%B1%82%EF%BC%9A%EF%BC%881%EF%BC%89%EF%BD%9Cx%26%238321%3B%EF%BC%8Dx%26%238322%3B%EF%BD%9C%E5%92%8C%EF%BC%88x%26%238321%3B%2Bx%26%238322%3B%EF%BC%89%2F2%EF%BC%882%EF%BC%89x%26%238321%3B%E7%9A%84%E4%B8%89%E6%AC%A1%E6%96%B9%2Bx%26%238322%3B%E7%9A%84%E4%B8%89%E6%AC%A1%E6%96%B9)
一元二次方程ax²+bx+c=0(a≠0)的两根为x₁和x₂.求:(1)|x₁-x₂|和(x₁+x₂)/2(2)x₁的三次方+x₂的三次方
一元二次方程ax²+bx+c=0(a≠0)的两根为x₁和x₂.求:
(1)|x₁-x₂|和(x₁+x₂)/2
(2)x₁的三次方+x₂的三次方
一元二次方程ax²+bx+c=0(a≠0)的两根为x₁和x₂.求:(1)|x₁-x₂|和(x₁+x₂)/2(2)x₁的三次方+x₂的三次方
|x₁-x₂|=√(x1-x2)²=√[(x1+x2)²-4x1x2]=√(b²/a²-4c/a)
x₁+x₂)/2=-2b/a
(2)
x1³+x2³=(x1+x2)³-3x1x2(x1+x2)=-b³/a³+3bc/a²