\(\dfrac{9x-7}{\sqrt{4x+5}}=\sqrt{7x+5}\) (1) \(\Leftrightarrow9x-7=\sqrt{\left(7x+5\right)\left(4x+5\right)}\) \(\Leftrightarrow9x-7=\sqrt{28x^2+35x+20x+25}\) \(\Leftrightarrow9x-7=\sqrt{28x^2+55x+25}\) \(\Leftrightarrow\sqrt{28x^2+55x+25}=9x-7\) \(\Leftrightarrow\sqrt{28x^2+55x+25}=\left(9x-7\right)^2\) \(\Leftrightarrow28x^2+55x+25=81x^2-126x+49\) \(\Leftrightarrow28x^2+55x+25-81x^2+126x-49=0\) \(\Leftrightarrow-53x^2+181x-24=0\) \(\Leftrightarrow53x^2-181x+24=0\) \(\Leftrightarrow x=\dfrac{-\left(-181\right)\pm\sqrt{\left(-181\right)^2-4\cdot53\cdot24}}{2\cdot53}\) \(\Leftrightarrow x=\dfrac{181\pm\sqrt{32761-5088}}{106}\) \(\Leftrightarrow x=\dfrac{181\pm\sqrt{27673}}{106}\) \(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{181+\sqrt{27673}}{106}\\x=\dfrac{181-\sqrt{27673}}{106}\end{matrix}\right.\) Sau khi dùng phép thử ta nhận thấy \(x\ne\dfrac{181-\sqrt{27673}}{106}\) Vậy tập nghiệm phương trình (1) là \(S=\left\{\dfrac{181+\sqrt{27673}}{106}\right\}\)Câu trả lời: \(\dfrac{9x-7}{\sqrt{4x+5}}=\sqrt{7x+5}\) (1) \(\Leftrightarrow9x-7=\sqrt{\left(7x+5\right)\left(4x+5\right)}\) \(\Leftrightarrow9x-7=\sqrt{28x^2+35x+20x+25}\) \(\Leftrightarrow9x-7=\sqrt{28x^2+55x+25}\) \(\Leftrightarrow\sqrt{28x^2+55x+25}=9x-7\) \(\Leftrightarrow\sqrt{28x^2+55x+25}=\left(9x-7\right)^2\) \(\Leftrightarrow28x^2+55x+25=81x^2-126x+49\) \(\Leftrightarrow28x^2+55x+25-81x^2+126x-49=0\) \(\Leftrightarrow-53x^2+181x-24=0\) \(\Leftrightarrow53x^2-181x+24=0\) \(\Leftrightarrow x=\dfrac{-\left(-181\right)\pm\sqrt{\left(-181\right)^2-4\cdot53\cdot24}}{2\cdot53}\) \(\Leftrightarrow x=\dfrac{181\pm\sqrt{32761-5088}}{106}\) \(\Leftrightarrow x=\dfrac{181\pm\sqrt{27673}}{106}\) \(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{181+\sqrt{27673}}{106}\\x=\dfrac{181-\sqrt{27673}}{106}\end{matrix}\right.\) Sau khi dùng phép thử ta nhận thấy \(x\ne\dfrac{181-\sqrt{27673}}{106}\) Vậy tập nghiệm phương trình (1) là \(S=\left\{\dfrac{181+\sqrt{27673}}{106}\right\}\)