a) ĐKXĐ: \(x\ne2;4\)
\(\dfrac{x-3}{x-2}-\dfrac{x-2}{x-4}\) = \(\dfrac{16}{5}\)
<=> \(\dfrac{\left(x-3\right)\left(x-4\right)-\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x-4\right)}\) = \(\dfrac{16}{5}\)
<=> \(\dfrac{x^2-7x+12-x^2+4x-4}{\left(x-2\right)\left(x-4\right)}-\dfrac{16}{5}\) = 0
<=> \(\dfrac{5\left(-3x+8\right)}{5\left(x-2\right)\left(x-4\right)}-\dfrac{16\left(x^2-6x+8\right)}{5\left(x-2\right)\left(x-4\right)}\) = 0
=> \(-15x+40-16x^2+96x-128\) = 0
<=> \(-\left(16x^2-81x+88\right)\) = 0
<=> \(16x^2-81x+88\) = 0
<=> \(\left(16x^2-81x+\dfrac{6561}{64}\right)-\dfrac{929}{64}\) = 0
<=> \(\left(4x-\dfrac{81}{8}\right)^2\) = \(\dfrac{929}{64}\)
<=> \(\left[{}\begin{matrix}4x-\dfrac{81}{8}=\sqrt{\dfrac{929}{64}}\\4x-\dfrac{81}{8}=-\sqrt{\dfrac{929}{64}}\end{matrix}\right.\) <=> \(\left[{}\begin{matrix}x=\dfrac{81+\sqrt{929}}{32}\\x=\dfrac{81-\sqrt{929}}{32}\end{matrix}\right.\)
Vậy .......................................... ( số xấu nhỉ!)
b) \(2x^2-6x+1\) = 0
<=> \(2\left(x^2-3x+\dfrac{9}{4}\right)-\dfrac{7}{2}\) = 0
<=> \(2\left(x-\dfrac{3}{2}\right)^2\) = \(\dfrac{7}{2}\)
<=> \(\left(x-\dfrac{3}{2}\right)^2\) = \(\dfrac{7}{4}\)
<=> \(\left[{}\begin{matrix}x-\dfrac{3}{2}=\sqrt{\dfrac{7}{4}}\\x-\dfrac{3}{2}=-\sqrt{\dfrac{7}{4}}\end{matrix}\right.\) <=> \(\left[{}\begin{matrix}x=\dfrac{3+\sqrt{7}}{2}\\x=\dfrac{3-\sqrt{7}}{2}\end{matrix}\right.\)
Vậy .............................
c) \(3x^2+12x-66\) = 0
<=> \(3\left(x^2+4x+4\right)-78\) = 0
<=> \(3\left(x+2\right)^2\) = 78
<=> \(\left(x+2\right)^2\) = 26
<=> \(\left[{}\begin{matrix}x+2=\sqrt{26}\\x+2=-\sqrt{26}\end{matrix}\right.\) <=> \(\left[{}\begin{matrix}x=-2+\sqrt{26}\\x=-2-\sqrt{26}\end{matrix}\right.\)
Vậy .................................
P/s: Yahoooooooooooooo.......xong rồi!