Question

(6-x)^3-x^2(16-x)=2x^2+116

Answer 1

Пошаговое объяснение:

(6 - x)³ - x² (16 - x) = 2x² + 116,

216 - 108х + 18х² - х³ - 16х² + х³ = 2х² + 116,

216 - 108х + 18х² - 16х² - 2х² - 116 = 0,

216 - 108х - 116 = 0,

108х = 216 - 116,

108х = 100,

х = 100/108,

х = 25/27

Answer 2

To solve the equation (6-x)^3 - x^2(16-x) = 2x^2 + 116, follow these steps:

Step 1: Expand the left-hand side of the equation.

(6-x)^3 = (6-x)(6-x)(6-x) = (36 - 12x + x^2)(6-x) = 216 - 72x + 6x^2 - 6x^2 + 2x^3 (6-x)^3 = 2x^3 - 72x + 216

x^2(16-x) = 16x^2 - x^3

So, the equation becomes: 2x^3 - 72x + 216 - 16x^2 + x^3 = 2x^2 + 116

Step 2: Simplify and combine like terms.

Combine the x^3 terms: 3x^3 - 72x + 216 - 16x^2 = 2x^2 + 116

Step 3: Bring all the terms to one side of the equation to set it to zero.

3x^3 - 16x^2 - 2x^2 - 72x + 216 - 116 = 0

Step 4: Combine like terms again:

3x^3 - 18x^2 - 72x + 100 = 0

Step 5: Now, we need to solve for x. Unfortunately, there is no analytical solution to this cubic equation that can be expressed using simple algebraic operations. You would typically use numerical methods to approximate the solutions. Some common numerical methods for finding roots of equations include the Newton-Raphson method, the bisection method, or graphical methods.

If you need a specific numerical approximation for the solutions, you can use software or calculators capable of solving cubic equations. Alternatively, if you have access to a programming language or mathematical software, you can implement one of the numerical methods mentioned above to find the approximate values of x that satisfy the equation.