Question

·leg½ (x² - x - 2) = -2 ​

Answer 1

Ответ: x1=3; x2=-2

Пошаговое объяснение:

По определению логарифма

(1/2)$^-^2 =x^2-x-2$

x²-x-2-4=0

x²-x-6=0

x1=3; x2=-2 ( по т Виета)

Answer 2

To solve the equation $\frac{{\sqrt{2}x}}{2} (x^2 - x - 2) = -2$, first, let's simplify the equation:

$\frac{{\sqrt{2}x}}{2} (x^2 - x - 2) = -2$

Now, expand $\frac{{\sqrt{2}x}}{2} (x^2 - x - 2)$:

$\frac{{\sqrt{2}x}}{2} \cdot x^2 - \frac{{\sqrt{2}x}}{2} \cdot x - \frac{{\sqrt{2}x}}{2} \cdot 2 = -2$

Simplify further:

$\frac{{\sqrt{2}x^3}}{2} - \frac{{\sqrt{2}x^2}}{2} - \sqrt{2}x = -2$

Now, we have a cubic equation:

$\frac{{\sqrt{2}x^3}}{2} - \frac{{\sqrt{2}x^2}}{2} - \sqrt{2}x + 2 = 0$

To solve this cubic equation, you can use numerical methods or software tools as finding exact solutions might be complex. If you need an approximate solution, you can use numerical methods like the Newton-Raphson method or use software like Mathematica, MATLAB, or graphing calculators that can handle equations symbolically or numerically.