Đáp án:
Giải thích các bước giải:
$(\frac{1}{4}-x^2)-3x=0\\\Leftrightarrow x^2+3x-\frac{1}{4}=0\\\Leftrightarrow 4x^2+12x-1=0\\\Leftrightarrow x=\frac{-3\pm \sqrt{10}}{2}$
b) $|2x-3|+|y-5|=0\\\Leftrightarrow |2x-3|=-|y-5|\\TH1: 2x-3=-|y-5|\\\Leftrightarrow x=\frac{3-|y-5|}{2}\\TH2: 2x-3=|y-5|\\\Leftrightarrow x=\frac{3+|y-5|}{2}\\\Rightarrow \left[\begin{array}{l}x=\frac{3-|y-5|}{2}\\x=\frac{3+|y-5|}{2}\end{array}\right.$
c) $(2x-3)^2=36\\\Leftrightarrow 2x-3=\pm 6\\\Leftrightarrow 2x=\pm 6+3\\\Leftrightarrow x=\frac{\pm 6+3}{2}\\\Rightarrow \left[\begin{array}{l}x=-\frac{3}{2}\\x=\frac{9}{2}\end{array}\right.$
d) $|2x+1|+\frac{2}{3}=2\\\Leftrightarrow |2x+1|=\frac{4}{3}\\TH1: 2x+1=\frac{4}{3}\\\Leftrightarrow x=\frac{1}{6}\\TH2: 2x+1=-\frac{7}{6}\\\Rightarrow \left[\begin{array}{l}x=\frac{1}{6}\\x=-\frac{7}{6}\end{array}\right.$
e) $7^x+2\times 7^x+2=357\\\Leftrightarrow 3\times 7^x+2=357\\\Leftrightarrow 7^x=\frac{355}{3}\\\Leftrightarrow x\approx 2,453096564$
