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Popular >

x(3+x)^4+(3-x)^4=386

Solution

x (3 + x)^{4} + (3 - x)^{4} = 386

Solution

x \approx - 1.45604 \dots, x \approx 1.20325 \dots, x \approx - 10.46386 \dots

Solution steps

x (3 + x)^{4} + (3 - x)^{4} = 386

Expand

x (3 + x)^{4} + (3 - x)^{4} : x^{5} + 13 x^{4} + 42 x^{3} + 162 x^{2} - 27 x + 81

x^{5} + 13 x^{4} + 42 x^{3} + 162 x^{2} - 27 x + 81 = 386

Move

386

to the left side

x^{5} + 13 x^{4} + 42 x^{3} + 162 x^{2} - 27 x - 305 = 0

Find one solution for

x^{5} + 13 x^{4} + 42 x^{3} + 162 x^{2} - 27 x - 305 = 0

using Newton-Raphson:

x \approx - 1.45604 \dots

Apply long division:

\frac{x ^{5} + 13 x ^{4} + 42 x ^{3} + 162 x ^{2} - 27 x - 305}{x + 1.45604 \dots} = x^{4} + 11.54395 \dots x^{3} + 25.19148 \dots x^{2} + 125.32007 \dots x - 209.47161 \dots

x^{4} + 11.54395 \dots x^{3} + 25.19148 \dots x^{2} + 125.32007 \dots x - 209.47161 \dots \approx 0

Find one solution for

x^{4} + 11.54395 \dots x^{3} + 25.19148 \dots x^{2} + 125.32007 \dots x - 209.47161 \dots = 0

using Newton-Raphson:

x \approx 1.20325 \dots

Apply long division:

\frac{x ^{4} + 11.54395 \dots x ^{3} + 25.19148 \dots x ^{2} + 125.32007 \dots x - 209.47161 \dots}{x - 1.20325 \dots} = x^{3} + 12.74720 \dots x^{2} + 40.52962 \dots x + 174.08752 \dots

x^{3} + 12.74720 \dots x^{2} + 40.52962 \dots x + 174.08752 \dots \approx 0

Find one solution for

x^{3} + 12.74720 \dots x^{2} + 40.52962 \dots x + 174.08752 \dots = 0

using Newton-Raphson:

x \approx - 10.46386 \dots

Apply long division:

\frac{x ^{3} + 12.74720 \dots x ^{2} + 40.52962 \dots x + 174.08752 \dots}{x + 10.46386 \dots} = x^{2} + 2.28334 \dots x + 16.63701 \dots

x^{2} + 2.28334 \dots x + 16.63701 \dots \approx 0

Find one solution for

x^{2} + 2.28334 \dots x + 16.63701 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 1.45604 \dots, x \approx 1.20325 \dots, x \approx - 10.46386 \dots

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