Question

Помогите решить, не могу понять... $sqrt{x} =6-x$

Answer 1

$sqrt{x} =6-x Leftrightarrow left{begin{matrix} 6-x geq 0\ ( sqrt{x} ) ^{2} =(6-x)^2 end{matrix}right. Leftrightarrow left{begin{matrix} x leq 6 \ x=36-12x+x^2 end{matrix}right. Leftrightarrow \ \ \ Leftrightarrow left{begin{matrix} x leq 6\ x^2-13x+36=0 end{matrix}right. Leftrightarrow left{begin{matrix} xleq 6\ begin{bmatrix} x=9 \ x=4 end{matrix} end{matrix}right. Leftrightarrow x=4 \ \ \ OTBET: x=4$