Question

Giải phương trình:

\(\sqrt{4x-20}+3\sqrt{\frac{x-5}{9}}-\frac{1}{3}\sqrt{9x-45}=4\)

Answer 1

Giải:

\(\sqrt{4x-20}\) + 3\(\sqrt{\frac{x-5}{9}}\) - \(\frac{1}{3}\)\(\sqrt{9x-45}\)= 4

\(\Leftrightarrow\)\(\sqrt{4\left(x-5\right)}\) + 3\(\frac{\sqrt{x-5}}{\sqrt{9}}\)-\(\frac{1}{3}\)\(\sqrt{9\left(x-5\right)}\)=4

\(\Leftrightarrow\)\(\sqrt{4}\)\(\sqrt{x-5}\)+ 3\(\frac{\sqrt{x-5}}{3}\)-\(\frac{1}{3}\)\(\sqrt{9}\)\(\sqrt{x-5}\)= 4

\(\Leftrightarrow\)2\(\sqrt{x-5}\)+ 1\(\sqrt{x-5}\)-1\(\sqrt{x-5}\)=4

\(\Leftrightarrow\)( 2 + 1 - 1)\(\sqrt{x-5}\)= 4

\(\Leftrightarrow\)2\(\sqrt{x-5}\)= 4

\(\Leftrightarrow\)\(\sqrt{x-5}\)= 2 . Đk : x \(\ge\)5

\(\Rightarrow\)x - 5 = 4

\(\Leftrightarrow\)x = 9 ( thỏa mãn )

Vậy phương trình đã cho có tập nghiệm S = \(\left\{9\right\}\)