16s^3 - 18s^2 + 10s - 3 = 0
asked by guest
You asked:
Solve the equation
16 s 3 − 18 s 2 + 10 s − 3 = 0 16 {s}^{3} - 18 {s}^{2} + 10 s - 3 = 0 16 s 3 − 18 s 2 + 10 s − 3 = 0 for the variable
s s s .
MathBot Answer:
The 3 solutions to the equation are:
s = 3 8 + 15 512 + 1551 1152 3 − 13 192 15 512 + 1551 1152 3 ≈ 0.60419174 s = − 15 512 + 1551 1152 3 2 + 13 384 15 512 + 1551 1152 3 + 3 8 + i ( 13 3 384 15 512 + 1551 1152 3 + 3 15 512 + 1551 1152 3 2 ) ≈ 0.26040413 + 0.49246486 i s = − 15 512 + 1551 1152 3 2 + 13 384 15 512 + 1551 1152 3 + 3 8 + i ( − 3 15 512 + 1551 1152 3 2 − 13 3 384 15 512 + 1551 1152 3 ) ≈ 0.26040413 − 0.49246486 i \begin{aligned}s &= \frac{3}{8} + \sqrt[3]{\frac{15}{512} + \frac{\sqrt{1551}}{1152}} - \frac{13}{192 \sqrt[3]{\frac{15}{512} + \frac{\sqrt{1551}}{1152}}} \approx 0.60419174\\s &= - \frac{\sqrt[3]{\frac{15}{512} + \frac{\sqrt{1551}}{1152}}}{2} + \frac{13}{384 \sqrt[3]{\frac{15}{512} + \frac{\sqrt{1551}}{1152}}} + \frac{3}{8} + i \left(\frac{13 \sqrt{3}}{384 \sqrt[3]{\frac{15}{512} + \frac{\sqrt{1551}}{1152}}} + \frac{\sqrt{3} \sqrt[3]{\frac{15}{512} + \frac{\sqrt{1551}}{1152}}}{2}\right) \approx 0.26040413 + 0.49246486 i\\s &= - \frac{\sqrt[3]{\frac{15}{512} + \frac{\sqrt{1551}}{1152}}}{2} + \frac{13}{384 \sqrt[3]{\frac{15}{512} + \frac{\sqrt{1551}}{1152}}} + \frac{3}{8} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{15}{512} + \frac{\sqrt{1551}}{1152}}}{2} - \frac{13 \sqrt{3}}{384 \sqrt[3]{\frac{15}{512} + \frac{\sqrt{1551}}{1152}}}\right) \approx 0.26040413 -0.49246486 i\end{aligned} s s s = 8 3 + 3 512 15 + 1152 1551 − 192 3 512 15 + 1152 1551 13 ≈ 0.60419174 = − 2 3 512 15 + 1152 1551 + 384 3 512 15 + 1152 1551 13 + 8 3 + i 384 3 512 15 + 1152 1551 13 3 + 2 3 3 512 15 + 1152 1551 ≈ 0.26040413 + 0.49246486 i = − 2 3 512 15 + 1152 1551 + 384 3 512 15 + 1152 1551 13 + 8 3 + i − 2 3 3 512 15 + 1152 1551 − 384 3 512 15 + 1152 1551 13 3 ≈ 0.26040413 − 0.49246486 i
i i i imaginary unit , defined as i 2 = − 1 i^2 = -1 i 2 = − 1
