Question

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

Answer 1

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