Question

\(\sqrt{16x-32}+\sqrt{25x-50}=187\sqrt{9x-18}\)

\(\frac{\sqrt{15}+\sqrt{3}}{\sqrt{5}+1}+\frac{4}{1-\sqrt{3}}\)

Answer 1

\(\sqrt{16x-32}+\sqrt{25x-50}=187\sqrt{9x-18}\)

\(\Leftrightarrow\sqrt{16\left(x-2\right)}+\sqrt{25\left(x-2\right)}=187\sqrt{9\left(x-2\right)}\)

\(\Leftrightarrow4\sqrt{x-2}+5\sqrt{x-2}=561\sqrt{x-2}\)

\(\Leftrightarrow552\sqrt{x-2}=0\)

\(\Leftrightarrow\sqrt{x-2}=0\)

\(\Leftrightarrow x-2=0\Leftrightarrow x=2\)

Answer 2

\(\frac{\sqrt{15}+\sqrt{3}}{\sqrt{5}+1}+\frac{4}{1-\sqrt{3}}\)

\(=\frac{\sqrt{3}\left(\sqrt{5}+1\right)}{\sqrt{5}+1}+\frac{4\left(1+\sqrt{3}\right)}{1-3}\)

\(=\sqrt{3}+\frac{4\left(1+\sqrt{3}\right)}{-2}\)

\(=\sqrt{3}-2-2\sqrt{3}=-2-\sqrt{3}\)