Question

X^3+29x-97=0
Solve this cubic equation

Answer 1

Answer:

-2.045

Step-by-step explanation:

x3+29x-97=0.

Here p=O,q=29,r=-97.

so,

a={ 97/2 + square root [(97)^2/4 + (29)^3/27]^1/3

                                               =(64.557)^1/3           =4.01

and

=(-8.557)^1/2

=-2.045

Answer 2

${x}^{3} + 29x - 97 = 0$

As,

$\sf Coefficient[f(x),x]>0 \\ \implies x_{1} \in \: ℝ$

$x _{1} = \sqrt[3]{ \frac{97}{2} + \sqrt{( \frac{97}{2} ) ^{2} + {( \frac{29}{3} )}^{3} } } + \sqrt[3]{ \frac{97}{2} - \sqrt{ {( \frac{97}{2} )}^{2} + {( \frac{29}{3} )}^{3} } }$

$x _{1} = \frac{ \sqrt[3]{10476 + 12 \sqrt{1054797} } + \sqrt[3]{10476 - 12 \sqrt{1054797} } }{6}$

$x_1 \approx 2.6806$