Question

Giải phương trình  \(0,5\sqrt{\frac{2}{x}}-\sqrt{\frac{8}{25x}}+\sqrt{\frac{1}{4x}}=\frac{1}{5}\)

Answer 1

Điều kiện : x > 0

pt <=> \(\left(0,5.\sqrt{2}-\sqrt{\frac{8}{25}} +\sqrt{\frac{1}{4}}\right).\sqrt{\frac{1}{x}}=\frac{1}{5}\)

<=> \(\left(\frac{\sqrt{2}}{2}-\frac{2\sqrt{2}}{5}+\frac{1}{2}\right).\sqrt{\frac{1}{x}}=\frac{1}{5}\)

<=> \(\frac{\sqrt{2}+5}{10}.\sqrt{\frac{1}{x}}=\frac{1}{5}\) <=>  \(\sqrt{\frac{1}{x}}=\frac{1}{5}:\frac{\sqrt{2}+5}{10}=\frac{2}{\sqrt{2}+5}\)

=> \(\sqrt{x}=\frac{\sqrt{2}+5}{2}\) => x =  \(\frac{\left(\sqrt{2}+5\right)^2}{4}\) (thỏa mãn)

Vậy....