What are the solutions to the equation x-*x^4=x^{12} ?

The solutions to the equation x-*x^4=x^{12} are x=0,x\approx 0.89298…

Find the zeros of x-*x^4=x^{12}

The zeros of x-*x^4=x^{12} are x=0,x\approx 0.89298…

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x - \cdot x^{4} = x^{12}

x = 0, x \approx 0.89298 \dots

Solution steps

x - x^{4} = x^{12}

Switch sides

x^{12} = x - x^{4}

Move

\cdot x^{4}

to the left side

x^{12} + x^{4} = x

Move

x

to the left side

x^{12} + x^{4} - x = 0

Factor

x^{12} + x^{4} - x : x (x^{11} + x^{3} - 1)

x (x^{11} + x^{3} - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{11} + x^{3} - 1 = 0

Solve

x^{11} + x^{3} - 1 = 0 : x \approx 0.89298 \dots

The solutions are

x = 0, x \approx 0.89298 \dots

x^{3} - 13 x^{2} = 0

m^{5} - 2 m^{4} - m + 2 = 0

x^{3} - 8 x + 6 = 0

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

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

What are the solutions to the equation x-*x^4=x^{12} ?
The solutions to the equation x-*x^4=x^{12} are x=0,x\approx 0.89298…
Find the zeros of x-*x^4=x^{12}
The zeros of x-*x^4=x^{12} are x=0,x\approx 0.89298…