Please write in detail, with steps and statements. thx.
I tried to solve it with cubic equation root formula[ X=A^1/3+B^1/3, A+B=-P，AB=-（Q/3）^3]，but it doesn't apply to this one. Couldn't work out A and B
How do I solve this one? THANKS A LOT GUYS!!
2006-12-20 22:41:39 · 9 answers · asked by DedB 2 in Science & Mathematics ➔ Mathematics
C'mon guys!!! THIS IS A MATH PROBLEM, plz don't give me calculators!! I want STEPS, how to solve it STEP BY STEP. THAX
I said I'v tried root formula.Wouldn't work!! Tell me other methods puuuuleeeeeeeeze!! THX!
2006-12-20 23:32:20 · update #1
The reason the cubic equation root formula didn't work,
is because the discriminant is less than zero.
In these cases, you have to use trigonometry formulae.
Your equation, x^3 - 3x + 1 = 0 is represented by
x^3 + ax^2 + bx + c, where a = 0, b = -3 and c = 1.
Then, Q = (3b - a^2) / 9 = -1
and, R = (9ab - 27c - 2a^3) / 54 = -1/2
Discriminant = Q^3 + R^2 = -3/4, which is negative.
--------------------
The formulae to use [where cos(θ) = R / √(-Q^3)] are :
x1 = 2√(-Q) * cos(θ / 3) - a/3
x2 = 2√(-Q) * cos(θ / 3 + 120º) - a/3
x3 = 2√(-Q) * cos(θ / 3 + 240º) - a/3
--------------------
Here, cos(θ) = (-1/2) / √[-(-1)^3)] = -1/2,
so, θ = 120º.
Thus,
x1 = 2cos(40º) = 1.5321
x2 = 2cos(160º) = -1.8794
x3 = 2cos(280º) = 0.3473
2006-12-21 00:25:20 · answer #1 · answered by falzoon 7 · 1⤊ 0⤋
make x=u+v, u and v two new variables.
Substitute in the equation.
partition the equaiton in two parts:
1: u^3+v^3+1=0
2: 3*u*v*(u+v)-3*(u+v)=0
From 2), you get u*v=1. Substitute u=1/v in 1), and solve for v to obtain a quadratic equation for v^3 (v cubed).
from there,
v^3=1/2 (+-) 1/2*sqrt(3)*I, where I is hte imaginary number.
From here you get 6 possible answers, becasue of the +-. However, whenever you solve for x, you will come to only 3 of them.
Obtain the complex numbers of the cubic roots, remember that
u^3=1/2 (+-) 1/2*sqrt(3)*I, because their sum should equal 1, and from there you should obtain the x. Do this for the 3 possible answers.
check the webpages:
2006-12-21 00:27:21 · answer #2 · answered by David E 1 · 0⤊ 0⤋
First you have to open the brackets. As there is a negative sign before the bracket, all the terms in the barcket change their signs. 5X-(3X-1) = 0 Opening the brackets 5X -3X +1 = 0 Solve for X 2X +1 = 0 When you shift any term from one side of the equation to the other, it alters its sign. Therefore, 2X = 0-1 2X = -1 To find the value of X, shift 2 to the other side of the equation X= -1/2
2016-03-29 02:24:15 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Roots are:
1.53208888623796
-1.87938524157182
0.34729635533386
Which suggests that there isn't an easy way to factorise the equation. Either that or you've written the question down wrong.
If you want to cheat and just get the answer (like I did, after struggling to factorise it) use the first link below. The second link talks you through the methodology, in a reasonably clear fashion.
2006-12-20 23:03:05 · answer #4 · answered by robcraine 4 · 0⤊ 0⤋
Just put the equation in the graphic calculator and sketch the graph, find out the x-intercepts and they are the values of x.
2006-12-20 23:03:20 · answer #5 · answered by Miss. Anonymous 2 · 0⤊ 0⤋
Use the rational root theorem:
http://en.wikipedia.org/wiki/Rational_root_theorem
Good luck.
2006-12-20 23:03:38 · answer #6 · answered by Jerry P 6 · 0⤊ 0⤋
x^3-3x+1=0
x^3+1=3x
(x+1)(x^2-x+1)=3x
and that's all i got...
sorry....
2006-12-21 00:11:04 · answer #7 · answered by Anonymous · 0⤊ 0⤋
Need help with homework?
2006-12-20 22:43:10 · answer #8 · answered by Just me. 4 · 0⤊ 0⤋
Maybe find your answer here: http://en.wikipedia.org/wiki/Cubic_equation
2006-12-20 23:13:57 · answer #9 · answered by Duliner 4 · 0⤊ 0⤋