What are the solutions to the equation x^3+x^4=10 ?

The solutions to the equation x^3+x^4=10 are x\approx 1.57237…,x\approx-2.09209…

Find the zeros of x^3+x^4=10

The zeros of x^3+x^4=10 are x\approx 1.57237…,x\approx-2.09209…

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x^{3} + x^{4} = 10

x \approx 1.57237 \dots, x \approx - 2.09209 \dots

Solution steps

x^{3} + x^{4} = 10

Move

10

to the left side

x^{3} + x^{4} - 10 = 0

Write in the standard form

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

x^{4} + x^{3} - 10 = 0

Find one solution for

x^{4} + x^{3} - 10 = 0

using Newton-Raphson:

x \approx 1.57237 \dots

Apply long division:

\frac{x ^{4} + x ^{3} - 10}{x - 1.57237 \dots} = x^{3} + 2.57237 \dots x^{2} + 4.04472 \dots x + 6.35981 \dots

x^{3} + 2.57237 \dots x^{2} + 4.04472 \dots x + 6.35981 \dots \approx 0

Find one solution for

x^{3} + 2.57237 \dots x^{2} + 4.04472 \dots x + 6.35981 \dots = 0

using Newton-Raphson:

x \approx - 2.09209 \dots

Apply long division:

\frac{x ^{3} + 2.57237 \dots x ^{2} + 4.04472 \dots x + 6.35981 \dots}{x + 2.09209 \dots} = x^{2} + 0.48028 \dots x + 3.03993 \dots

x^{2} + 0.48028 \dots x + 3.03993 \dots \approx 0

Find one solution for

x^{2} + 0.48028 \dots x + 3.03993 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.57237 \dots, x \approx - 2.09209 \dots

x^{4} - 9 x^{2} = 0

x^{5} = 25

x^{4} - 8 x^{2} - 9 = 0

(x^{2} - 6 x)^{2} + 2 \cdot (x - 3)^{2} = 81

6 x^{7} - 8 = 2 (7 - 10)

What are the solutions to the equation x^3+x^4=10 ?
The solutions to the equation x^3+x^4=10 are x\approx 1.57237…,x\approx-2.09209…
Find the zeros of x^3+x^4=10
The zeros of x^3+x^4=10 are x\approx 1.57237…,x\approx-2.09209…