What are the solutions to the equation 10^4=x^4-(x-0.5)^4 ?

The solutions to the equation 10^4=x^4-(x-0.5)^4 are x\approx 17.34854…

Find the zeros of 10^4=x^4-(x-0.5)^4

The zeros of 10^4=x^4-(x-0.5)^4 are x\approx 17.34854…

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1 0^{4} = x^{4} - (x - 0.5)^{4}

x \approx 17.34854 \dots

Solution steps

1 0^{4} = x^{4} - (x - 0.5)^{4}

Expand

1 0^{4} : 10000

Expand

x^{4} - (x - 0.5)^{4} : 2 x^{3} - 1.5 x^{2} + 0.5 x - 0.0625

10000 = 2 x^{3} - 1.5 x^{2} + 0.5 x - 0.0625

Switch sides

2 x^{3} - 1.5 x^{2} + 0.5 x - 0.0625 = 10000

Move

10000

to the left side

2 x^{3} - 1.5 x^{2} + 0.5 x - 10000.0625 = 0

Find one solution for

2 x^{3} - 1.5 x^{2} + 0.5 x - 10000.0625 = 0

using Newton-Raphson:

x \approx 17.34854 \dots

Apply long division:

\frac{2 x ^{3} - 1.5 x ^{2} + 0.5 x - 10000.0625}{x - 17.34854 \dots} = 2 x^{2} + 33.19708 \dots x + 576.42094 \dots

2 x^{2} + 33.19708 \dots x + 576.42094 \dots \approx 0

Find one solution for

2 x^{2} + 33.19708 \dots x + 576.42094 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 17.34854 \dots

4 x^{1} + 4 x^{2} + 2 x^{3} = 4

5 x^{4} = 2560 x

2 r^{3} + 7 r^{2} - 4 r - 21 = 0

(1 + 0.0239193)^{1} = (1 + x)^{3}

8 x^{3} - 12 x^{2} + 6 x - 65 = 0

What are the solutions to the equation 10^4=x^4-(x-0.5)^4 ?
The solutions to the equation 10^4=x^4-(x-0.5)^4 are x\approx 17.34854…
Find the zeros of 10^4=x^4-(x-0.5)^4
The zeros of 10^4=x^4-(x-0.5)^4 are x\approx 17.34854…