Question

2*x^3-4*x^2-3*x+6 = 0

Answer 1

Вроде все нормально видно

Answer 2

To solve the equation 2x^3 - 4x^2 - 3*x + 6 = 0, we need to find the values of x that satisfy this equation. Unfortunately, this equation is a cubic equation, which means it may not have simple, easy-to-find solutions like linear or quadratic equations.

One way to solve this cubic equation is to use numerical methods or computational tools to approximate the roots. However, I can walk you through the general steps of solving a cubic equation manually using Cardano's formula. Keep in mind that this method involves complex numbers and can be quite involved.

Let's start by simplifying the equation and getting it into the standard form:

2x^3 - 4x^2 - 3*x + 6 = 0

Now, we'll make a substitution to eliminate the quadratic term. Let's set y = x - b/3, where b is the coefficient of the quadratic term, which is -4 in this case:

2*(y + b/3)^3 - 4*(y + b/3)^2 - 3*(y + b/3) + 6 = 0

Expanding and simplifying:

2*(y^3 + (b^2/3)y + (2b^3/27)) - 4(y^2 + (2b/3)y + (b^2/9)) - 3(y + b/3) + 6 = 0

Now, we have:

2*y^3 + (2b^3/27) + (b^2/3)*y - (8b^2/9)*y - (4b/3)y + (8b/9) - 3y - b + 6 = 0

Simplifying further:

2*y^3 + (b^2/3)*y - (4b/3)*y + (2b^3/27) - (8b^2/9)y - b + (8b/9) - 3y + 6 = 0

Now, the cubic equation is in the standard form: 2*y^3 + (b^2/3)*y - (8b^2/9)y - 3y + (2b^3/27) - b + (8b/9) + 6 = 0

Now, we have to find the value of b and then use Cardano's formula to solve for y. After finding y, we can obtain the solutions for x using the original substitution.

However, note that manually solving cubic equations using Cardano's formula can be quite tedious and might involve complex numbers, especially if the cubic does not have real roots. For practical purposes, numerical methods or computational tools are often preferred to approximate the solutions of cubic equations.