What are the solutions to the equation u^4u^2-2=7u ?

The solutions to the equation u^4u^2-2=7u are u\approx-0.28563…,u\approx 1.52726…

Find the zeros of u^4u^2-2=7u

The zeros of u^4u^2-2=7u are u\approx-0.28563…,u\approx 1.52726…

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u^{4} u^{2} - 2 = 7 u

u \approx - 0.28563 \dots, u \approx 1.52726 \dots

Solution steps

u^{4} u^{2} - 2 = 7 u

Refine

u^{6} - 2 = 7 u

Move

7 u

to the left side

u^{6} - 2 - 7 u = 0

Write in the standard form

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

u^{6} - 7 u - 2 = 0

Find one solution for

u^{6} - 7 u - 2 = 0

using Newton-Raphson:

u \approx - 0.28563 \dots

Apply long division:

\frac{u ^{6} - 7 u - 2}{u + 0.28563 \dots} = u^{5} - 0.28563 \dots u^{4} + 0.08158 \dots u^{3} - 0.02330 \dots u^{2} + 0.00665 \dots u - 7.00190 \dots

u^{5} - 0.28563 \dots u^{4} + 0.08158 \dots u^{3} - 0.02330 \dots u^{2} + 0.00665 \dots u - 7.00190 \dots \approx 0

Find one solution for

u^{5} - 0.28563 \dots u^{4} + 0.08158 \dots u^{3} - 0.02330 \dots u^{2} + 0.00665 \dots u - 7.00190 \dots = 0

using Newton-Raphson:

u \approx 1.52726 \dots

Apply long division:

\frac{u ^{5} - 0.28563 \dots u ^{4} + 0.08158 \dots u ^{3} - 0.02330 \dots u ^{2} + 0.00665 \dots u - 7.00190 \dots}{u - 1.52726 \dots} = u^{4} + 1.24163 \dots u^{3} + 1.97789 \dots u^{2} + 2.99746 \dots u + 4.58459 \dots

u^{4} + 1.24163 \dots u^{3} + 1.97789 \dots u^{2} + 2.99746 \dots u + 4.58459 \dots \approx 0

Find one solution for

u^{4} + 1.24163 \dots u^{3} + 1.97789 \dots u^{2} + 2.99746 \dots u + 4.58459 \dots = 0

using Newton-Raphson:

No Solution for

u \in R

The solutions are

u \approx - 0.28563 \dots, u \approx 1.52726 \dots

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(1 + 0.02)^{12} = (1 + x)^{4}

m (m - 1) (m - 2) (m - 3) = 840

2 x^{3} + 4 x = 6 x^{2}

5 y^{3} - 44 y^{2} - 9 y = 0

What are the solutions to the equation u^4u^2-2=7u ?
The solutions to the equation u^4u^2-2=7u are u\approx-0.28563…,u\approx 1.52726…
Find the zeros of u^4u^2-2=7u
The zeros of u^4u^2-2=7u are u\approx-0.28563…,u\approx 1.52726…