Question

What is the solution of startroot x 12 endroot = x?

Answer 1

Answer:

x = 0  ;  x = 1

Step-by-step explanation:

$\sqrt{x^{12}} =x$

$\Longleftrightarrow \sqrt{x^{6\times 2}} =x$

$\Longleftrightarrow \sqrt{\left( x^{6}\right)^{2} } =x$

$\Longleftrightarrow |x^{6}|=x$

$\Longleftrightarrow x^{6}=x\ \ \ ;\ |x^{6}|=x^{6}$

$\Longleftrightarrow x^{6}-x=0$

$\Longleftrightarrow x(x^{5}-1)=0$

$\Longleftrightarrow x=0 \ \ or\ \ (x^{5}-1)=0$

$\Longleftrightarrow x=0\ \ or\ \ x^{5}=1$

$\Longleftrightarrow x=0\ \ or\ \ x=1$