Step 1

Solve the radical

\(\displaystyle\sqrt{{{x}+{16}}}-\sqrt{{{x}-{4}}}={2}\)

Step 2

\(\displaystyle\sqrt{{{x}+{16}}}-\sqrt{{{x}-{4}}}={2}\)

\(\displaystyle\Rightarrow\sqrt{{{x}+{16}}}=\sqrt{{{x}-{4}}}+{2}\)

squaring both sides

\(\displaystyle{\left(\sqrt{{{x}+{16}}}\right)}^{{{2}}}={\left(\sqrt{{{x}-{4}}}+{2}\right)}^{{{2}}}\)

Expanding both sides

\(\displaystyle{x}+{16}={x}-{4}+{2}{\left(\sqrt{{{x}-{4}}}\right)}{\left({2}\right)}+{4}\ \ \ {\left[{\left({a}+{b}\right)}^{{{2}}}={a}^{{{2}}}+{2}{a}{b}+{b}^{{{2}}}\right]}\)

\(\displaystyle\Rightarrow{x}+{16}={x}+{4}\sqrt{{{x}-{4}}}\)

\(\displaystyle\Rightarrow{16}={4}\sqrt{{{x}-{4}}}\)

\(\displaystyle\Rightarrow{\frac{{{16}}}{{{4}}}}=\sqrt{{{x}-{4}}}\)

\(\displaystyle\Rightarrow{4}=\sqrt{{{x}-{4}}}\)

squaring both sides

16=x-4

\(\displaystyle\Rightarrow{20}={x}\)

Solve the radical

\(\displaystyle\sqrt{{{x}+{16}}}-\sqrt{{{x}-{4}}}={2}\)

Step 2

\(\displaystyle\sqrt{{{x}+{16}}}-\sqrt{{{x}-{4}}}={2}\)

\(\displaystyle\Rightarrow\sqrt{{{x}+{16}}}=\sqrt{{{x}-{4}}}+{2}\)

squaring both sides

\(\displaystyle{\left(\sqrt{{{x}+{16}}}\right)}^{{{2}}}={\left(\sqrt{{{x}-{4}}}+{2}\right)}^{{{2}}}\)

Expanding both sides

\(\displaystyle{x}+{16}={x}-{4}+{2}{\left(\sqrt{{{x}-{4}}}\right)}{\left({2}\right)}+{4}\ \ \ {\left[{\left({a}+{b}\right)}^{{{2}}}={a}^{{{2}}}+{2}{a}{b}+{b}^{{{2}}}\right]}\)

\(\displaystyle\Rightarrow{x}+{16}={x}+{4}\sqrt{{{x}-{4}}}\)

\(\displaystyle\Rightarrow{16}={4}\sqrt{{{x}-{4}}}\)

\(\displaystyle\Rightarrow{\frac{{{16}}}{{{4}}}}=\sqrt{{{x}-{4}}}\)

\(\displaystyle\Rightarrow{4}=\sqrt{{{x}-{4}}}\)

squaring both sides

16=x-4

\(\displaystyle\Rightarrow{20}={x}\)