Question

(x-1)^3-x(x+2)^2+x(7x-5)=6​

Answer 1

Если что-то не понятно - спрашивай

Answer 2

To solve the equation $(x-1)^3 - x(x+2)^2 + x(7x-5) = 6$, we'll first expand the expressions and then simplify the equation. Let's proceed step by step:

Step 1: Expand the terms $(x-1)^3$ expands to $x^3 - 3x^2 + 3x - 1$. $x(x+2)^2$ expands to $x(x^2 + 4x + 4) = x^3 + 4x^2 + 4x$. $x(7x-5)$ expands to $7x^2 - 5x$.

Step 2: Rewrite the equation with the expanded expressions: $x^3 - 3x^2 + 3x - 1 - (x^3 + 4x^2 + 4x) + (7x^2 - 5x) = 6$

Step 3: Combine like terms: $x^3 - 3x^2 + 3x - 1 - x^3 - 4x^2 - 4x + 7x^2 - 5x = 6$

Step 4: Simplify the equation: $x^3 - x^2 - 6x - 1 = 6$

Step 5: Move all terms to one side to set the equation to zero: $x^3 - x^2 - 6x - 7 = 0$

Now we have a cubic equation. Unfortunately, finding exact solutions for general cubic equations can be challenging. However, we can still attempt to solve it numerically or use approximation methods.

One approach to finding a solution is by using numerical methods such as graphing, the Newton-Raphson method, or iterative methods. Graphing the equation will give you an idea of where the solutions might be located. The Newton-Raphson method and other iterative methods can provide approximate solutions for the equation.

If you provide a specific value for $x$, I can help you evaluate the left-hand side of the equation to verify whether it satisfies the equation. Otherwise, without a specific value or further constraints, we can't find exact solutions.