Question

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

Answer 1

x = 0 ; x = 1

Explanation:

`\sqrt{x^(12)} =x`

`\Longleftrightarrow \sqrt{x^(6* 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`