What are the solutions to the equation x^1-x^2+x^3=1,x^1-2x^2=2 ?

The solutions to the equation x^1-x^2+x^3=1,x^1-2x^2=2 are x=1,x=i,x=-i

Find the zeros of x^1-x^2+x^3=1,x^1-2x^2=2

The zeros of x^1-x^2+x^3=1,x^1-2x^2=2 are x=1,x=i,x=-i

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x^{1} - x^{2} + x^{3} = 1, x^{1} - 2 x^{2} = 2

x = 1, x = i, x = - i

Solution steps

x^{1} - x^{2} + x^{3} = 1

Refine

x - x^{2} + x^{3} = 1

Move

1

to the left side

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

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

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

Factor

x^{3} - x^{2} + x - 1 : (x - 1) (x^{2} + 1)

(x - 1) (x^{2} + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{2} + 1 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{2} + 1 = 0 : x = i, x = - i

The solutions are

x = 1, x = i, x = - i

x^{3} = 1000

x^{3} - 2 x - 15 = 0

z^{6} + 2 i = 0

(x - 1) (x - 2) (x^{2} - 3 x) = 24

x^{2} + 11 x^{24} = 0

What are the solutions to the equation x^1-x^2+x^3=1,x^1-2x^2=2 ?
The solutions to the equation x^1-x^2+x^3=1,x^1-2x^2=2 are x=1,x=i,x=-i
Find the zeros of x^1-x^2+x^3=1,x^1-2x^2=2
The zeros of x^1-x^2+x^3=1,x^1-2x^2=2 are x=1,x=i,x=-i