What are the solutions to the equation x^3-x^2=4x^2-8x+4 ?

The solutions to the equation x^3-x^2=4x^2-8x+4 are x=1,x=2

Find the zeros of x^3-x^2=4x^2-8x+4

The zeros of x^3-x^2=4x^2-8x+4 are x=1,x=2

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x^{3} - x^{2} = 4 x^{2} - 8 x + 4

x = 1, x = 2

Solution steps

x^{3} - x^{2} = 4 x^{2} - 8 x + 4

Move

4

to the left side

x^{3} - x^{2} - 4 = 4 x^{2} - 8 x

Move

8 x

to the left side

x^{3} - x^{2} - 4 + 8 x = 4 x^{2}

Move

4 x^{2}

to the left side

x^{3} - 5 x^{2} + 8 x - 4 = 0

Factor

x^{3} - 5 x^{2} + 8 x - 4 : (x - 1) (x - 2)^{2}

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x - 2 = 0

Solve

x - 1 = 0 : x = 1

Solve

x - 2 = 0 : x = 2

The solutions are

x = 1, x = 2

m^{4} - 1 = 0

x - 4 = - 2 x^{3}

4 x^{3} - 3 x^{2} + 4 x + 11 = 0

x^{3} - 6 x^{2} - 6 x - 2 = 0

(4 x)^{3} = 4^{3^{3}}

What are the solutions to the equation x^3-x^2=4x^2-8x+4 ?
The solutions to the equation x^3-x^2=4x^2-8x+4 are x=1,x=2
Find the zeros of x^3-x^2=4x^2-8x+4
The zeros of x^3-x^2=4x^2-8x+4 are x=1,x=2