x的三次方加上x的平方减x再减2等于0其实算式是 X3+X2-X–2=0 x3次方-x平方+2怎么分解因式啊
\u6c42X3-X-2=0\u7684\u89e3\uff1f\u8fd9\u4e2a\u5c31\u8981\u7528\u5230\u7acb\u65b9\u5dee\u516c\u5f0f\u4e86\uff0cx^3-x-2=0
\u6362\u4e3a\uff1ax^3-1-x-1=0
\u5373\uff1a\uff08x^3-1\uff09-(x+1)=0
x^3-1=(x+1)(x^2-x-1)\u8fd9\u4e2a\u5c31\u662f\u7acb\u65b9\u5dee\u516c\u5f0f\uff0c\u5982\u679c\u4e0d\u61c2\uff0c\u53ea\u80fd\u5b66\u7740\u51d1\u9879
\u6240\u4ee5\u539f\u5f0f\u4e3a\uff08x+1\uff09(x^2-x-1-1)=0
\u5373\uff08x+1\uff09(x-2)(x+1)=0
\u6240\u4ee5x=1,x=-1,x=2
\u8fd9\u4e2a\u9700\u8981\u586b\u9879\u624d\u53ef\u4ee5\u5206\u89e3\u7684\uff0c\u6846\u91cc\u9762\u7684\u662f\u6dfb\u52a0\u7684\u9879
【解三次方程要用此公式,预测你的方程只有一实根,具体过程略,请看】
一元三次方程aX^3+bX^2+cX+d=0,(a,b,c,d∈R,且a≠0).
重根判别式:
A=b^2-3ac;
B=bc-9ad;
C=c^2-3bd,
总判别式:Δ=B^2-4AC.
当A=B=0时,盛金公式①:
X1=X2=X3=-b/(3a)=-c/b=-3d/c.
当Δ=B^2-4AC>0时,盛金公式②:
X1=(-b-(Y1)^(1/3)-(Y2)^(1/3))/(3a);
X2,3=(-2b+(Y1)^(1/3)+(Y2)^(1/3))/(6a)±i3^(1/2)((Y1)^(1/3)-(Y2)^(1/3))/(6a),
其中Y1,2=Ab+3a(-B±(B^2-4AC)^(1/2))/2,i^2=-1.
当Δ=B^2-4AC=0时,盛金公式③:
X1=-b/a+K;X2=X3=-K/2,
其中K=B/A,(A≠0).
当Δ=B^2-4AC<0时,盛金公式④:
X1=
(-b-2A^(1/2)cos(θ/3))/(3a);
X2,3=
(-b+A^(1/2)(cos(θ/3)±3^(1/2)sin(θ/3)))/(3a),
其中θ=arccosT,T=
(2Ab-3aB)/(2A^(3/2)),(A>0,-1<T<1).
2.盛金判别法
①:当A=B=0时,方程有一个三重实根;
②:当Δ=B^2-4AC>0时,方程有一个实根和一对共轭虚根;
③:当Δ=B^2-4AC=0时,方程有三个实根,其中有一个两重根;
④:当Δ=B^2-4AC<0时,方程有三个不相等的实根.
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