What are the solutions to the equation 3x^8-4x^3=4 ?

The solutions to the equation 3x^8-4x^3=4 are x\approx 1.16768…,x\approx-0.88995…

Find the zeros of 3x^8-4x^3=4

The zeros of 3x^8-4x^3=4 are x\approx 1.16768…,x\approx-0.88995…

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3 x^{8} - 4 x^{3} = 4

x \approx 1.16768 \dots, x \approx - 0.88995 \dots

Solution steps

3 x^{8} - 4 x^{3} = 4

Move

4

to the left side

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

Find one solution for

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

using Newton-Raphson:

x \approx 1.16768 \dots

Apply long division:

\frac{3 x ^{8} - 4 x ^{3} - 4}{x - 1.16768 \dots} = 3 x^{7} + 3.50304 \dots x^{6} + 4.09043 \dots x^{5} + 4.77631 \dots x^{4} + 5.57720 \dots x^{3} + 2.51239 \dots x^{2} + 2.93367 \dots x + 3.42559 \dots

3 x^{7} + 3.50304 \dots x^{6} + 4.09043 \dots x^{5} + 4.77631 \dots x^{4} + 5.57720 \dots x^{3} + 2.51239 \dots x^{2} + 2.93367 \dots x + 3.42559 \dots \approx 0

Find one solution for

3 x^{7} + 3.50304 \dots x^{6} + 4.09043 \dots x^{5} + 4.77631 \dots x^{4} + 5.57720 \dots x^{3} + 2.51239 \dots x^{2} + 2.93367 \dots x + 3.42559 \dots = 0

using Newton-Raphson:

x \approx - 0.88995 \dots

Apply long division:

\frac{3 x ^{7} + 3.50304 \dots x ^{6} + 4.09043 \dots x ^{5} + 4.77631 \dots x ^{4} + 5.57720 \dots x ^{3} + 2.51239 \dots x ^{2} + 2.93367 \dots x + 3.42559 \dots}{x + 0.88995 \dots} = 3 x^{6} + 0.83316 \dots x^{5} + 3.34894 \dots x^{4} + 1.79589 \dots x^{3} + 3.97893 \dots x^{2} - 1.02869 \dots x + 3.84916 \dots

3 x^{6} + 0.83316 \dots x^{5} + 3.34894 \dots x^{4} + 1.79589 \dots x^{3} + 3.97893 \dots x^{2} - 1.02869 \dots x + 3.84916 \dots \approx 0

Find one solution for

3 x^{6} + 0.83316 \dots x^{5} + 3.34894 \dots x^{4} + 1.79589 \dots x^{3} + 3.97893 \dots x^{2} - 1.02869 \dots x + 3.84916 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.16768 \dots, x \approx - 0.88995 \dots

x^{3} + 12 x^{2} + 36 x = 0

x^{4} - 13 x^{2} = - 36

y^{3} + 3 y^{2} = 16 y + 48

6 x^{2} - x^{3} = 0

3 x^{3} - 4 x^{2} + 75 x - 100 = 0

What are the solutions to the equation 3x^8-4x^3=4 ?
The solutions to the equation 3x^8-4x^3=4 are x\approx 1.16768…,x\approx-0.88995…
Find the zeros of 3x^8-4x^3=4
The zeros of 3x^8-4x^3=4 are x\approx 1.16768…,x\approx-0.88995…