What are the solutions to the equation -1=2t-t^3 ?

The solutions to the equation -1=2t-t^3 are t=-1,t=(1+sqrt(5))/2 ,t=(1-sqrt(5))/2

Find the zeros of -1=2t-t^3

The zeros of -1=2t-t^3 are t=-1,t=(1+sqrt(5))/2 ,t=(1-sqrt(5))/2

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- 1 = 2 t - t^{3}

t = - 1, t = \frac{1 + 5}{2}, t = \frac{1 - 5}{2}

Decimal Notation

t = - 1, t = 1.61803 \dots, t = - 0.61803 \dots

Solution steps

- 1 = 2 t - t^{3}

Switch sides

2 t - t^{3} = - 1

Move

1

to the left side

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

Write in the standard form

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

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

t + 1 = 0 : t = - 1

Solve

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

The solutions are

t = - 1, t = \frac{1 + 5}{2}, t = \frac{1 - 5}{2}

x^{3} + 40 = 25

x^{3} = 6 x + 9

a, a^{2} (ba - b + 1 - a^{2}) = 0

m^{3} + 2 m^{2} + 4 m + 8 = 0

5 x^{4} - 1 = 0

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