What are the solutions to the equation 8x^3-8x^2+1=0 ?

The solutions to the equation 8x^3-8x^2+1=0 are x= 1/2 ,x=(1+sqrt(5))/4 ,x=(1-sqrt(5))/4

Find the zeros of 8x^3-8x^2+1=0

The zeros of 8x^3-8x^2+1=0 are x= 1/2 ,x=(1+sqrt(5))/4 ,x=(1-sqrt(5))/4

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8 x^{3} - 8 x^{2} + 1 = 0

x = \frac{1}{2}, x = \frac{1 + 5}{4}, x = \frac{1 - 5}{4}

Decimal Notation

x = 0.5, x = 0.80901 \dots, x = - 0.30901 \dots

Solution steps

8 x^{3} - 8 x^{2} + 1 = 0

Factor

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

(2 x - 1) (4 x^{2} - 2 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 x - 1 = 0 or 4 x^{2} - 2 x - 1 = 0

Solve

2 x - 1 = 0 : x = \frac{1}{2}

Solve

4 x^{2} - 2 x - 1 = 0 : x = \frac{1 + 5}{4}, x = \frac{1 - 5}{4}

The solutions are

x = \frac{1}{2}, x = \frac{1 + 5}{4}, x = \frac{1 - 5}{4}

x^{3} - 7 = 0

\frac{x ^{3}}{2} = 8

- 8 + 3 X^{3} + 2 X = 0

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

x^{3} + 2 x^{2} + 5 x = 0

What are the solutions to the equation 8x^3-8x^2+1=0 ?
The solutions to the equation 8x^3-8x^2+1=0 are x= 1/2 ,x=(1+sqrt(5))/4 ,x=(1-sqrt(5))/4
Find the zeros of 8x^3-8x^2+1=0
The zeros of 8x^3-8x^2+1=0 are x= 1/2 ,x=(1+sqrt(5))/4 ,x=(1-sqrt(5))/4