1,求X的值a)X^3-6X^2+11X-6=0b)X^4-10X^3+35X^2-50X+24=0c)X^5-15X^4+85X^3-225X^2+274X-120=02,determine and explain patterns in the roots.意思就是确定并且解释是什么模式在这个根中3,conjecture(hypothesize) clues in the equation that

来源：学生作业帮助网 编辑：六六作业网 时间：2024/11/26 20:34:47
1,求X的值a)X^3-6X^2+11X-6=0b)X^4-10X^3+35X^2-50X+24=0c)X^5-15X^4+85X^3-225X^2+274X-120=02,determineande

1,求X的值a)X^3-6X^2+11X-6=0b)X^4-10X^3+35X^2-50X+24=0c)X^5-15X^4+85X^3-225X^2+274X-120=02,determine and explain patterns in the roots.意思就是确定并且解释是什么模式在这个根中3,conjecture(hypothesize) clues in the equation that
1,求X的值
a)X^3-6X^2+11X-6=0
b)X^4-10X^3+35X^2-50X+24=0
c)X^5-15X^4+85X^3-225X^2+274X-120=0
2,determine and explain patterns in the roots.
意思就是确定并且解释是什么模式在这个根中
3,conjecture(hypothesize) clues in the equation that can help you predict patterns in the roots.
4,test your conjecture on the following equations:
a)X^3-7X+6=0
b)X^4-X^3-7X^2+13X-6=0
c)X^6-21X^5+175X^4+1624X^2-1764X+720=0

1,求X的值a)X^3-6X^2+11X-6=0b)X^4-10X^3+35X^2-50X+24=0c)X^5-15X^4+85X^3-225X^2+274X-120=02,determine and explain patterns in the roots.意思就是确定并且解释是什么模式在这个根中3,conjecture(hypothesize) clues in the equation that
1,求X的值
a)X^3-6X^2+11X-6=0
x^3-6x^2+9x+2x-6=0
x(x-3)^2+2(x-3)=0
(x-3)(x^2-3x+2)=0
x1=3,x2=1,x3=2(三个不等实根）
b)X^4-10X^3+35X^2-50X+24=0
x^4-x^3-9x^3+9x^2+26x^2-26x-24x+24=0
x^3(x-1)-9x^2(x-1)+26x(x-1)-24(x-1)=0
(x-1)(x^3-9x^2+26x-24)=0
(x-1)[x^2(x-2)-7x(x-2)+12(x-2)]=0
(x-1)(x-2)(x^2-7x+12)=0
x1=1,x2=2,x3=3,x4=3
c)X^5-15X^4+85X^3-225X^2+274X-120=0
仿上面的方法,换一种写知
令f(x)=x^5-15x^4+85x^3-225x^2+274x-120
则f(1)=1-15+85-225+274-120=0,故x1=1
x^5-15x^4+85x^3-225x^2+274x-120=(x-1)(x^4-14x^3+71x^2-154x+120)
同理,x=2时,x^4-14x^3+71x^2-154x+120=0
x^4-14x^3+71x^2-154x+120=（x-2)(x^3-12x^2+47x-60)
x^3-12x^2+47x-60=（x-3)(x-9x+27)
所以x1=1,x2=2,x3=3,x4,5=(9+/-3根号3倍i)/2(三实根,两虚根）
4,仿第一题做法知
a)X^3-7X+6=0
（x-1)(x^2+x-6)=0
(x-1)(x-2)(x+3)=0
x1=1,x2=2,x3=-3
b)X^4-X^3-7X^2+13X-6=0
(x-1)(x^3-7x+6)=0
x1=x2=1,x3=2,x4=-3
c)X^6-21X^5+175X^4+1624X^2-1764X+720=0(应该还有-735x^3吧）
(x-1)(x^5-20x^4+155x^3-580x^2+1044x-720)=0
(x-1)(x-2)(x^4-18x^3+119x^2-342x+360)=0
(x-1)(x-2)(x-3)(x^3-15x^2+74x-120)=0
(x-1)(x-2)(x-3)(x-4)(x^2-11x+30)=0
(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)=0
x1=1,x2=2,x3=3,x4=4,x5=5,x6=6
(以上用计算机更方便）

（1） x-3/x-2 - x-5/x-4=x-7/x-6 - x-9/x-8(2) 已知x+3/(x-2)^2=A/x-2 + B/(x-2)^2 ,求A和B的值. 已知1+x+x^2+x^3=0,求x+x^2+x^3+x^4+x^+x^6+x^7+x^8的值 如果1+x+x^2+x^3=0,求x+x^2+X^3+x^4+x^5+x^6+x^7+x^8的值, 若(A/x+2)+(B/x-3)=7x-1/x^2-x-6,求A,B的值 一个“整式的乘法”的问题请先阅读下列解题过程,再仿做下面的问题.已知X*X + X - 1=0,求X*X*X + 2*X*X + 3的值.解X*X*X + 2X*X +3=X*X*X +X*X -X +X*X +X +3=X{X*X +X -1} +X*X +X -1 +4=0+0+4=4+ x + X*X + X*X*X=0.+ X*X + X*X*X 若x*x+x+1+0,求x^7+2x^6+x^5+x^4+x^3+x*x+1的值 求：2X^3+X^2-X-2=A(X-1)(X-2)(X-3)+BX(X-2)(X-3)+CX(X-1)(X-3)+DX(X-1)(X-2),求实数A,B,C,D的值 已知a^3X=1/27,求a^2x+ a^-2 x/a^x+a^-x的值 已知a^3X=1/27,求a^2x+ a^-2 x/a^x+a^-x的值 已知关于x的方程x=a+x/2+x/6+x/12+x/20+...+x/9900的解为x=-1,求a的值 已知a=x^3-5x^2,b=x^2-11x+6,求 当x=-1时,求a-5b的值 已知a(x*x+x-c)+b(2x*x-x-2)=7x*x+4x+3x.求a,b,c的值 (x*x+ax+b)(2x*x-3x-1)的积中,x*x*x项的系数为-5,x*x项的系数为-6 求a,b的值 解一道初一的分式方程（x+1)/(x+2)+(x+6)/(x+7)=(x+2)/(x+3)+(x+5)/(x+6)求x的值 A/x-1+B/x+2+C/x-3=x²+2x+5/(x-1)(x+2)(x-3)求ABC的值 已知x平方-3x-1=0,求代数式2x的三次方-3x的平方-11x+8的值.x²=3x+1所以x³=x(x²)=x(3x+1)=3x²+x=3(3x+1)+x=10x+3原式=2(10x+3)-3(3x+1)-11x+8=20x+6-9x-3-11x+8=11 求x^2-3x/x^2-6x+9*x^2-11x+30/x^2-5x-1 ★已知a>0,a^2x=2根号2+3,求a^6x+a^-6x/a^x-a^-x的值★已知a>0,a^2x=2√2+3,求a^6x+a^-6x/a^x-a^-x的值.应该先把a^6x+a^-6x/a^x-a^-x化简吧.