What are the solutions to the equation x^4-(x-0.005)^4-0.1^4=0 ?

The solutions to the equation x^4-(x-0.005)^4-0.1^4=0 are x\approx 0.17348…

Find the zeros of x^4-(x-0.005)^4-0.1^4=0

The zeros of x^4-(x-0.005)^4-0.1^4=0 are x\approx 0.17348…

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x^{4} - (x - 0.005)^{4} - 0. 1^{4} = 0

x \approx 0.17348 \dots

Solution steps

x^{4} - (x - 0.005)^{4} - 0. 1^{4} = 0

Expand

x^{4} - (x - 0.005)^{4} - 0. 1^{4} : 0.02 x^{3} - 0.00015 x^{2} + 0.0000005 x - 0.00010 \dots

0.02 x^{3} - 0.00015 x^{2} + 0.0000005 x - 0.00010 \dots = 0

Find one solution for

0.02 x^{3} - 0.00015 x^{2} + 0.0000005 x - 0.00010 \dots = 0

using Newton-Raphson:

x \approx 0.17348 \dots

Apply long division:

\frac{0.02 x ^{3} - 0.00015 x ^{2} + 0.0000005 x - 0.00010 \dots}{x - 0.17348 \dots} = 0.02 x^{2} + 0.00331 \dots x + 0.00057 \dots

0.02 x^{2} + 0.00331 \dots x + 0.00057 \dots \approx 0

Find one solution for

0.02 x^{2} + 0.00331 \dots x + 0.00057 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.17348 \dots

x^{3} + 3 x^{2} + 9 x + 27

4 x^{3} - 8 x + 1 = 0

2 m x^{4} + 3 n x^{4} + 10 m + 15 n

A, A^{4} t = m - R^{2}

x^{3} + 4 x

What are the solutions to the equation x^4-(x-0.005)^4-0.1^4=0 ?
The solutions to the equation x^4-(x-0.005)^4-0.1^4=0 are x\approx 0.17348…
Find the zeros of x^4-(x-0.005)^4-0.1^4=0
The zeros of x^4-(x-0.005)^4-0.1^4=0 are x\approx 0.17348…