Question

X2+1/3-4x-x2/12 = x2-4/9

Answer 1

Ответ:

Для начала сократим дробь :

$\frac{1}{3} - 4x - \frac{2}{12} x = - \frac{4}{9}$

Дальше вычисляем всё суммированное :

$\frac{1}{3} - 4x - \frac{1}{6}x = - \frac{4}{9}$

Дальше умножаем все обе части :

$\frac{1}{3} - \frac{25}{6}x = - \frac{4}{9}$

После перенесем нашу константу в правую часть уравнения :

$6 - 75x = - 8$

Все вычисляем :

$- 75x = - 14$

И получаем окончательный ответ на уравнение :

$x = \frac{14}{75}$

Надеюсь помог, удачи! :)

Answer 2

To solve the given equation, let's first simplify it step by step:

$x^2 + \frac{1}{3} - 4x - \frac{x^2}{12} = x^2 - \frac{4}{9}$.

First, let's combine like terms on the left side of the equation:

$x^2 - \frac{x^2}{12} - 4x + \frac{1}{3} = x^2 - \frac{4}{9}$.

Now, to eliminate the fractions, let's find a common denominator for $\frac{x^2}{12}$ and $\frac{1}{3}$. The least common multiple of 12 and 3 is 12. So, we can rewrite the equation as follows:

$\frac{12x^2}{12} - \frac{x^2}{12} - \frac{48x}{12} + \frac{4}{12} = \frac{12x^2}{12} - \frac{16}{12}$.

Simplifying further:

$\frac{11x^2 - 48x + 4}{12} = \frac{12x^2 - 16}{12}$.

Now, cross-multiply to get rid of the fractions:

$11x^2 - 48x + 4 = 12x^2 - 16$.

Move all terms to one side of the equation:

$12x^2 - 11x^2 - 48x + 16 - 4 = 0$.

Simplifying further:

$x^2 - 48x + 12 = 0$.

This is a quadratic equation in the form $ax^2 + bx + c = 0$, where $a = 1$, $b = -48$, and $c = 12$. To solve this quadratic equation, you can use the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Plugging in the values:

$x = \frac{48 \pm \sqrt{(-48)^2 - 4(1)(12)}}{2(1)}$.

$x = \frac{48 \pm \sqrt{2304 - 48}}{2}$.

$x = \frac{48 \pm \sqrt{2256}}{2}$.

$x = \frac{48 \pm 48\sqrt{14}}{2}$.

Now, you have two possible solutions for $x$:

1. $x = \frac{48 + 48\sqrt{14}}{2} = 24 + 24\sqrt{14}$.
2. $x = \frac{48 - 48\sqrt{14}}{2} = 24 - 24\sqrt{14}$