Question

81(1/3-1)(1/9х^2+1/3х+1)-3х(х-2)^2=12х^2​

Answer 1

Ответ:

Объяснение:

81*(x³/27-1)-3x(x²-4x+4)-12x²=0

3x³-81-3x³+12x²-12x-12x²=0

-12x-81=0

12x= -81

x= -6,75

Answer 2

To solve the equation, let's simplify and expand the expression on the left side:

81(1/3 - 1)(1/9x^2 + 1/3x + 1) - 3x(x - 2)^2 = 12x^2

First, simplify the expression inside the parentheses:

(1/3 - 1) = -2/3

(1/9x^2 + 1/3x + 1) can be simplified as follows:

1/9x^2 + 1/3x + 1 = (1/9)x^2 + (1/3)x + 1 = (x^2/9) + (x/3) + 1

Now we substitute these simplified expressions back into the equation:

81(-2/3)((x^2/9) + (x/3) + 1) - 3x(x - 2)^2 = 12x^2

Next, we expand the expression (x - 2)^2 using the FOIL method:

(x - 2)^2 = (x - 2)(x - 2) = x^2 - 2x - 2x + 4 = x^2 - 4x + 4

Substituting this back into the equation:

81(-2/3)((x^2/9) + (x/3) + 1) - 3x(x^2 - 4x + 4) = 12x^2

Now let's simplify further:

-2/3 * (x^2/9 + x/3 + 1) = -2/3 * (x^2/9) - 2/3 * (x/3) - 2/3 * (1) = -2x^2/27 - 2x/9 - 2/3

-3x(x^2 - 4x + 4) = -3x^3 + 12x^2 - 12x

Substituting these simplified expressions back into the equation:

81(-2x^2/27 - 2x/9 - 2/3) - 3x(x^2 - 4x + 4) = 12x^2

Now distribute the multiplication:

-2x^2 * (81/27) - 2x * (81/9) - 2 * (81/3) - 3x^3 + 12x^2 - 12x = 12x^2

Simplifying further:

-6x^2 - 18x - 54 - 3x^3 + 12x^2 - 12x = 12x^2

Combine like terms:

(-3x^3 - 6x^2 + 12x^2) + (-18x - 12x) - 54 = 12x^2

Simplify:

-3x^3 + 6x^2 - 30x - 54 = 12x^2

Rearrange the equation to bring all terms to one side:

-3x^3 + 6x^2 - 12x^2 - 30x - 54 - 12x^2 = 0

Combine like terms:

-3x^3 - 18x^2 - 30x - 54 = 0

Unfortunately, this equation does not factor easily, and the solutions may require numerical methods or approximation techniques.