What are the solutions to the equation a^3-a^7-5-3=0 ?

The solutions to the equation a^3-a^7-5-3=0 are a\approx-1.40428…

Find the zeros of a^3-a^7-5-3=0

The zeros of a^3-a^7-5-3=0 are a\approx-1.40428…

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a^{3} - a^{7} - 5 - 3 = 0

a \approx - 1.40428 \dots

Solution steps

a^{3} - a^{7} - 5 - 3 = 0

Refine

- a^{7} + a^{3} - 8 = 0

Find one solution for

- a^{7} + a^{3} - 8 = 0

using Newton-Raphson:

a \approx - 1.40428 \dots

Apply long division:

\frac{- a ^{7} + a ^{3} - 8}{a + 1.40428 \dots} = - a^{6} + 1.40428 \dots a^{5} - 1.97201 \dots a^{4} + 2.76927 \dots a^{3} - 2.88884 \dots a^{2} + 4.05676 \dots a - 5.69685 \dots

- a^{6} + 1.40428 \dots a^{5} - 1.97201 \dots a^{4} + 2.76927 \dots a^{3} - 2.88884 \dots a^{2} + 4.05676 \dots a - 5.69685 \dots \approx 0

Find one solution for

- a^{6} + 1.40428 \dots a^{5} - 1.97201 \dots a^{4} + 2.76927 \dots a^{3} - 2.88884 \dots a^{2} + 4.05676 \dots a - 5.69685 \dots = 0

using Newton-Raphson:

No Solution for

a \in R

The solution is

a \approx - 1.40428 \dots

x^{17} = x

x, x^{4} + y^{2} + x^{2} y^{2} + 16 x^{2} - 10 x^{2} y = 0

x, x^{3} d^{2} - x^{2} d^{1} - 3 x y = x^{2}

x^{3} - 2 x^{2} = 75

\frac{x}{3} + \frac{3}{9} = x^{4} + 75

What are the solutions to the equation a^3-a^7-5-3=0 ?
The solutions to the equation a^3-a^7-5-3=0 are a\approx-1.40428…
Find the zeros of a^3-a^7-5-3=0
The zeros of a^3-a^7-5-3=0 are a\approx-1.40428…