6.1 Areas Between Curves/10

${\begin{aligned}&\color {red}\mathbf {y=1+{\sqrt {x}}} &\color {royalblue}\mathbf {y={\frac {3+x}{3}}} \\\\\end{aligned}}$

${\begin{aligned}1+{\sqrt {x}}&={\frac {3+x}{3}}\\1+{\sqrt {x}}-{\frac {3+x}{3}}&=0\\{\frac {3+3{\sqrt {x}}}{3}}-{\frac {3+x}{3}}&=0\\3+3{\sqrt {x}}-3+x&=0\\3{\sqrt {x}}+x&=0\\3{\sqrt {x}}&=-x\\9x&=x^{2}\\9x-x^{2}&=0\\x(9-x)&=0\\x&=0,9\end{aligned}}$