x^2-4ax+3a^2+2a-1=0公式法解方程设x1 x2是一元二次方程ax^2+bx+c=0(a不等于0)的两根求代数式a(x1^3+x2^3)+b(x1^2+x2^2)+c(x1+x2)的值
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![x^2-4ax+3a^2+2a-1=0公式法解方程设x1 x2是一元二次方程ax^2+bx+c=0(a不等于0)的两根求代数式a(x1^3+x2^3)+b(x1^2+x2^2)+c(x1+x2)的值](/uploads/image/z/7205445-45-5.jpg?t=x%5E2-4ax%2B3a%5E2%2B2a-1%3D0%E5%85%AC%E5%BC%8F%E6%B3%95%E8%A7%A3%E6%96%B9%E7%A8%8B%E8%AE%BEx1+x2%E6%98%AF%E4%B8%80%E5%85%83%E4%BA%8C%E6%AC%A1%E6%96%B9%E7%A8%8Bax%5E2%2Bbx%2Bc%3D0%EF%BC%88a%E4%B8%8D%E7%AD%89%E4%BA%8E0%EF%BC%89%E7%9A%84%E4%B8%A4%E6%A0%B9%E6%B1%82%E4%BB%A3%E6%95%B0%E5%BC%8Fa%EF%BC%88x1%5E3%2Bx2%5E3%EF%BC%89%2Bb%EF%BC%88x1%5E2%2Bx2%5E2%EF%BC%89%2Bc%EF%BC%88x1%2Bx2%EF%BC%89%E7%9A%84%E5%80%BC)
x^2-4ax+3a^2+2a-1=0公式法解方程设x1 x2是一元二次方程ax^2+bx+c=0(a不等于0)的两根求代数式a(x1^3+x2^3)+b(x1^2+x2^2)+c(x1+x2)的值
x^2-4ax+3a^2+2a-1=0公式法解方程
设x1 x2是一元二次方程ax^2+bx+c=0(a不等于0)的两根
求代数式a(x1^3+x2^3)+b(x1^2+x2^2)+c(x1+x2)的值
x^2-4ax+3a^2+2a-1=0公式法解方程设x1 x2是一元二次方程ax^2+bx+c=0(a不等于0)的两根求代数式a(x1^3+x2^3)+b(x1^2+x2^2)+c(x1+x2)的值
x^2-4ax+3a^2+2a-1=0
x={4a±√[(4a)^2-4(3a^2+2a-1)/2
x=2a±|a-1|
x =a+1或3a-1
x1 x2是一元二次方程ax^2+bx+c=0
x1+x2=-b/a
x1*x2=c/a
a(x1^3+x2^3)+b(x1^2+x2^2)+c(x1+x2)
=a(x1+x2)(x1^2-x1*x2+x2^2)+b[(x1+x2)^2-2x1*x2]+c(x1+x2)
=a(x1+x2)[(x1+x2)^2-3x1*x2]+b[(x1+x2)^2-2x1*x2]+c(x1+x2)
=a(-b/a)[(-b/a)^2-3c/a]+b[(-b/a)^2-2c/a]+c(-b/a)
=-b^3/a^2+3bc/a+b^3/a^2-2bc/a-bc/a
=0
x^2-4ax+3a^2+2a-1=0=x^2-4ax+(3a-1)(a+1)=(x-3a+1)(x-a-1)
x=3a-1 or a+1
x1*x2=-c/a
x1+x2=b/a
x1^3+x2^3=(x1+x2)(x1^2+x2^2-x1x2)=(x1+x2)[(x1+x2)^2-3x1x2]=(b/a)[(b/a)^2+3c/a]
a(x1^3+x2^3)+b(x1^2+x2^2)+c(x1+x2)=b(b^2+3ac)/a^2+b[(b/a)^2-2c/a]+bc/a
x^2-4ax+3a^2+2a-1=0
(x^2-4ax+4a^2)-(a^2-2a+1)=0
(x-2a)^2-(a-1)^2=0
(x-2a+a-1)(x-2a-a+1)=0
(x-a-1)(x-3a+1)=0
x=a+1或x=3a-1
设x1 x2是一元二次方程ax^2+bx+c=0(a不等于0)的两根
则x1+x2=-b/a x1...
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x^2-4ax+3a^2+2a-1=0
(x^2-4ax+4a^2)-(a^2-2a+1)=0
(x-2a)^2-(a-1)^2=0
(x-2a+a-1)(x-2a-a+1)=0
(x-a-1)(x-3a+1)=0
x=a+1或x=3a-1
设x1 x2是一元二次方程ax^2+bx+c=0(a不等于0)的两根
则x1+x2=-b/a x1*x2=c/a
x1^3+x2^3=(x1+x2)(x^2-x1x2+x^2)=(x1+x2)[(x1+x2)^2-3x1x2]
=(-b/a)[(-b/a)^2-3*(c/a)]=(b/a)[3c/a-b^2/a^2]=(3abc-b^3)/a^3
x1^2+x2^2=(x1+x2)^2-2x1x2=(-b/a)^2-2(c/a)=(b^2-2ac)/a^2
a(x1^3+x2^3)+b(x1^2+x2^2)+c(x1+x2)
=(3abc-c^3)/a^2+(b^3-2abc)/a^2+c^2/a
=(abc+b^3-c^3-ac^2)/a^2
=(b-c)(b^2+bc+c^2+ac)/a^2
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