Question

X^3+x+корень кубический (x^3+x-2)=12

Answer 1

Ловите решение. Тот кто его составлял, очень любит замены и фанат кубических уравнений lol
Единственный корень x=2.

Answer 2

To solve the equation $x^3 + x + \sqrt[3]{x^3 + x - 2} = 12$, we can follow these steps:

Step 1: Isolate the cube root term on one side of the equation. Step 2: Cube both sides to eliminate the cube root. Step 3: Simplify the resulting equation to a cubic equation. Step 4: Solve the cubic equation for $x$.

Let's go through each step in detail:

Step 1: Isolate the cube root term: Subtract $x$ and 12 from both sides of the equation to isolate the cube root term on the left side: $x^3 + \sqrt[3]{x^3 + x - 2} = 12 - x$

Step 2: Cube both sides: Raise both sides to the power of 3 to eliminate the cube root: $(x^3 + \sqrt[3]{x^3 + x - 2})^3 = (12 - x)^3$

Step 3: Simplify the resulting equation: Using the identity $(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$, we can expand the left side of the equation: $x^9 + 3x^7\sqrt[3]{x^3 + x - 2} + 3x^4(x^3 + x - 2) + (x^3 + x - 2) = 12^3 - 3 \cdot 12^2 x + 3 \cdot 12 x^2 - x^3$

Step 4: Solve the cubic equation for $x$: The equation after expanding and simplifying becomes a cubic equation in terms of $x^3$: $x^9 + 3x^7\sqrt[3]{x^3 + x - 2} + 3x^7 - 3x^4 + x^3 + x - 2 - 1728 + 432x - 36x^2 - x^3 = 0$

We can't solve this cubic equation directly due to its complexity. While there are numerical methods to find approximate solutions for $x$, it's not feasible to provide a specific numerical solution without more context or constraints on the value of $x$.

If you have specific values for $x$ that you want to evaluate in the equation, you can substitute those values and calculate the result. Alternatively, if you need an approximate solution for $x$, you can use numerical methods like Newton's method or other root-finding algorithms to find an approximation.