Question

(3x+1)^3=27x^2(x+1)+8x+2

Answer 1

9х+3=54х+54+8х+2

3-54-2=54х-8х-9х

-49=35х

-7=5х

х=-5/7

Ответ: х=-5/7

 

Answer 2

To solve the equation $(3x+1)^3 = 27x^2(x+1) + 8x + 2$, you can follow these steps:

Step 1: Expand the left side of the equation by cubing $(3x+1)$:

$(3x+1)^3 = (3x+1)(3x+1)(3x+1) = 27x^2(x+1) + 9x(x+1) + 3(x+1)$

Now, your equation becomes:

$27x^2(x+1) + 9x(x+1) + 3(x+1) = 27x^2(x+1) + 8x + 2$

Step 2: Simplify both sides of the equation by collecting like terms:

$27x^2(x+1) + 9x^2 + 9x + 3x + 3 = 27x^2(x+1) + 8x + 2$

Step 3: Subtract $27x^2(x+1)$ from both sides of the equation to eliminate the terms with $x^2$:

$9x^2 + 9x + 3x + 3 - 27x^2(x+1) = 8x + 2$

Step 4: Distribute the $-27x^2$ on the left side of the equation:

$9x^2 + 9x + 3x + 3 - 27x^3 - 27x^2 = 8x + 2$

Step 5: Combine like terms:

$9x^2 - 27x^3 - 18x^2 + 12x + 3 = 8x + 2$

Step 6: Move all terms to one side of the equation to set it equal to zero:

$9x^2 - 27x^3 - 18x^2 + 12x + 3 - 8x - 2 = 0$

Step 7: Simplify the equation:

$9x^2 - 27x^3 - 18x^2 + 12x + 1 = 0$

Step 8: Factor the equation. Notice that you can factor out a common factor of 9:

$9(x^2 - 3x^3 - 2x^2 + 4x + 1) = 0$

Step 9: Factor the polynomial inside the parentheses:

$x^2 - 3x^3 - 2x^2 + 4x + 1 = 0$

This equation is a cubic equation and can be a bit challenging to solve. You may try to use numerical methods or a graphing calculator to find approximate solutions.

Please note that I did not simplify the equation further, as the cubic equation inside the parentheses is not easily factorable by simple algebraic techniques.