Question

В каких случаях может быть верно равенство:
а)x=x²
б)x=x³
в)x²=x³
​

Answer 1

$\displaystyle a)\quad x=x^2\\\\x^2-x=0\\\\x(x-1)=0\\\\\boxed{\left[\begin{array}{ccc}x=0\\x=1\end{array}\right}\\\\\\b)\quad x=x^3\\\\x^3-x=0\\\\x(x^2-1)=0\\\\\left[\begin{array}{ccc}x=0\\x^2-1=0\end{array}\right\quad\rightarrow\quad\boxed{\left[\begin{array}{ccc}x=0\\x=1\\x=-1\end{array}\right}\\\\\\c)\quad x^2=x^3\\\\x^3-x^2=0\\\\x^2(x-1)=0\\\\\left[\begin{array}{ccc}x^2=0\\x-1=0\end{array}\right\quad\rightarrow\quad\boxed{\left[\begin{array}{ccc}x=0\\x=1\end{array}\right}$