Question

Tìm x,y

a)\(\left(\frac{2}{3}:x+\frac{1}{4}\right)^2=\frac{49}{64}\)

b)\(\frac{2}{5}:\)/x-2/-1/3=1/2

c)\(\frac{1}{8}-\left(\frac{1}{12}-\frac{1}{3}x\right)^3=0\)

Answer 1

a) \(\left(\frac{2}{3}:x+\frac{1}{4}\right)^2=\frac{49}{64}\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}\left(\frac{2}{3}:x+\frac{1}{4}\right)^2=\left(\frac{7}{8}\right)^2\\\left(\frac{2}{3}:x+\frac{1}{4}\right)^2=-\left(\frac{7}{8}\right)^2\end{array}\right.\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}\frac{2}{3}:x+\frac{1}{4}=\frac{7}{8}\\\frac{2}{3}:x+\frac{1}{4}=-\frac{7}{8}\end{array}\right.\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}\frac{2}{3}:x=\frac{5}{8}\\\frac{2}{3}:x=-\frac{9}{8}\end{array}\right.\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x=\frac{16}{15}\\x=-\frac{16}{27}\end{array}\right.\)

Answer 2

b) \(\frac{2}{5}:\left|x-2\right|-\frac{1}{3}=\frac{1}{2}\)

\(\Leftrightarrow\frac{2}{5}:\left|x-2\right|=\frac{5}{6}\)

\(\Leftrightarrow\left|x-2\right|=\frac{12}{25}\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x-2=\frac{12}{25}\\x-2=-\frac{12}{25}\end{array}\right.\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x=\frac{62}{25}\\x=\frac{38}{25}\end{array}\right.\)

Answer 3

c) \(\frac{1}{8}-\left(\frac{1}{12}-\frac{1}{3}x\right)^3=0\)

\(\Leftrightarrow\left(\frac{1}{12}-\frac{1}{3}x\right)^3=\frac{1}{8}\)

\(\Leftrightarrow\left(\frac{1}{12}-\frac{1}{3}x\right)^3=\left(\frac{1}{2}\right)^3\)

\(\Leftrightarrow\frac{1}{3}x=-\frac{5}{12}\)

\(\Leftrightarrow x=-\frac{5}{4}\)