[tex]\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[/tex][tex]\\\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 \}[/tex]
|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)
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Answers & Comments
[tex]\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[/tex][tex]\\\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 \}[/tex]
|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)