What are the solutions to the equation (x^3)/4 x+5/4 =4x ?

The solutions to the equation (x^3)/4 x+5/4 =4x are x\approx 0.31310…,x\approx 2.40563…

Find the zeros of (x^3)/4 x+5/4 =4x

The zeros of (x^3)/4 x+5/4 =4x are x\approx 0.31310…,x\approx 2.40563…

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\frac{x ^{3}}{4} x + \frac{5}{4} = 4 x

x \approx 0.31310 \dots, x \approx 2.40563 \dots

Solution steps

\frac{x ^{3}}{4} x + \frac{5}{4} = 4 x

Multiply both sides by

4

x^{4} + 5 = 16 x

Move

16 x

to the left side

x^{4} + 5 - 16 x = 0

Write in the standard form

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

x^{4} - 16 x + 5 = 0

Find one solution for

x^{4} - 16 x + 5 = 0

using Newton-Raphson:

x \approx 0.31310 \dots

Apply long division:

\frac{x ^{4} - 16 x + 5}{x - 0.31310 \dots} = x^{3} + 0.31310 \dots x^{2} + 0.09803 \dots x - 15.96930 \dots

x^{3} + 0.31310 \dots x^{2} + 0.09803 \dots x - 15.96930 \dots \approx 0

Find one solution for

x^{3} + 0.31310 \dots x^{2} + 0.09803 \dots x - 15.96930 \dots = 0

using Newton-Raphson:

x \approx 2.40563 \dots

Apply long division:

\frac{x ^{3} + 0.31310 \dots x ^{2} + 0.09803 \dots x - 15.96930 \dots}{x - 2.40563 \dots} = x^{2} + 2.71873 \dots x + 6.63830 \dots

x^{2} + 2.71873 \dots x + 6.63830 \dots \approx 0

Find one solution for

x^{2} + 2.71873 \dots x + 6.63830 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.31310 \dots, x \approx 2.40563 \dots

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

x^{3} = 0.5

m^{6} + 1 = 0

8 k^{6} + 15 k^{3} - 2 = 0

(\frac{x - 1}{3})^{3} = (\frac{1}{5})^{6}

What are the solutions to the equation (x^3)/4 x+5/4 =4x ?
The solutions to the equation (x^3)/4 x+5/4 =4x are x\approx 0.31310…,x\approx 2.40563…
Find the zeros of (x^3)/4 x+5/4 =4x
The zeros of (x^3)/4 x+5/4 =4x are x\approx 0.31310…,x\approx 2.40563…