Question

Найдите нули функции f=|3x-2|; g=|2s-1|+3; u=x4+x2

Answer 1

$1)~f=\left|3x-2\right|\medskip\\f=0\medskip\\\left|3x-2\right|=0\medskip\\3x-2=0\medskip\\x=\dfrac{2}{3}$

$2)~g=\left|2s-1\right|+3\medskip\\g=0\medskip\\\left|2s-1\right|+3=0\medskip\\\left|2s-1\right|=-3\medskip\\\left(\forall s\in\mathbb{R}\right)\left|2s-1\right|\geqslant 0 \Rightarrow \varnothing$

$3)~u=x^4+x^2\medskip\\u=0\medskip\\x^4+x^2=0\medskip\\x^2\left(x^2+1\right)=0\medskip\\\left[\begin{gathered}x^2=0\\x^2+1=0\end{gathered}\right.\Leftrightarrow\left[\begin{gathered}x=0\\\varnothing\end{gathered}\right.\Leftrightarrow x=0$