Question

Could I get the answer, all work, and explanation for this problem? Thanks

Answer 1

`\bf √(x+8)+√(x)=2\implies √(x+8)=2-√(x)\impliedby \textit{we raise both at }^2 \\\\\\ (√(x+8))^2=(2-√(x))^2\implies x+8=(2-√(x))(2-√(x)) \\\\\\ x+8=\stackrel{\textit{and we FOIL here}}{4-4√(x)+(√(x))^2}\implies x+8=4-4√(x)+x \\\\\\ 4=-4√(x)\implies \cfrac{4}{-4}=√(x)\implies -1=√(x)\impliedby \stackrel{again}{\textit{we raise both at }^2} \\\\\\ (-1)^2=(√(x))^2\implies 1=x`