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3 years ago

What is x3 - x2 - x + 1 = 0

Mathematics

2 answers:

Elina [12.6K]3 years ago

8 0

sorry i took so long to answer hope this helps you fam:)

x^3 +x^2 +x +1 = 0

=> x^2( x + 1) + 1(x + 1) = 0

=> (x^2 + 1)(x + 1) = 0

x + 1 = 0

=> x = -1

x^2 + 1 = 0

=> x^2 = -1

answer is...

x=1,x=-1

Reika [66]3 years ago

6 0

x^3-x^2-x+1=0

The answer to this problem is x=1, and x=-1.

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We can solve this via matrices, so the equations given can be written in matrix form as:

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Now I will shift rows to make my pivot point (top left) a 1 and so:

$\left[\begin{array}{cccc}1&-4&-1&-10\\2&1&2&15\\3&2&1&20\end{array}\right]$

Next I will come up with algorithms that can cancel out numbers where R1 means row 1, R2 means row 2 and R3 means row three therefore,

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$\left[\begin{array}{cccc}1&0&\frac{7}{9}&\frac{50}{9}\\0&1&\frac{4}{9}&\frac{35}{9}\\0&0&-\frac{20}{9}&-\frac{40}{9}\end{array}\right]$

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$-\frac{4}{9}R_3+R_2=R2$ , $-\frac{7}{9}R_3+R_1=R_1$

$\left[\begin{array}{cccc}1&0&0&4\\0&1&0&3\\0&0&1&2\end{array}\right]$

Therefore the solution to the system of equations are (x,y,z) = (4,3,2)

Note: If answer choices are given, plug them in and see if you get what is "equal to". Meaning plug in 4 for x, 3 for y and 2 for z in the first equation and you should get 20, second equation -10 and third 15.

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