Question

дам 15 баллов срочно уравнение с модулем
|x*x-2|*2.1 = 1.4

Answer 1

$\left | x^2-2 \right |\cdot 2,1=1,4\Leftrightarrow \left | x^2-2 \right |\cdot\frac{21}{10} =\frac{7}{5}\Leftrightarrow \left | x^2-2 \right |=\frac{7}{5}:\frac{21}{10}=\frac{7}{5}\cdot \frac{10}{21}\Leftrightarrow \\\Leftrightarrow \left | x^2-2 \right |=\frac{2}{3}\Leftrightarrow \left ( x^2-2 \right )^2=\left ( \frac{2}{3} \right )^2\Leftrightarrow \left ( x^2-2-\frac{2}{3} \right )\left ( x^2-2+\frac{2}{3} \right )=0\Leftrightarrow$$\\\Leftrightarrow \left ( x^2-\frac{8}{3} \right )\left ( x^2-\frac{4}{3} \right )=0\Rightarrow x=\left \{ \pm \frac{2}{\sqrt{3}},\pm 2\sqrt{\frac{2}{3}} \right \}$

Answer 2

|x^2-2|=1.4/2.1

|x^2-2|=2/3

3*|x^2-2|=2

1) |x^2-2|>=0 => 3*(x^2-2)=2

3*x^2-6=2

3*x^2=8

x^2=8/3

|x|=2*sqrt(2/3)

x1=2*sqrt(2/3)

x2=-2*sqrt(2/3).

2) |x^2-2|<0 => -3*(x^2-2)=2

x^2-2=-2/3

x^2=-2/3+2

x^2=(-2+6)/3

x^2=4/3

|x|=2/sqrt(3)

x3=2/sqrt(3)

x4=-2/sqrt(3)