Question

Tìm x biết:

\(\left(\frac{1}{x}-\frac{2}{3}\right)^2-\frac{1}{16}=0\)

mình đang cần gấp , ai nhanh mình tick

Answer 1

\(\left(\frac{1}{x}-\frac{2}{3}\right)^2-\frac{1}{16}=0\)

\(\Leftrightarrow\left(\frac{1}{x}-\frac{2}{3}\right)^2-\left(\frac{1}{4}\right)^2=0\)

\(\Leftrightarrow\left(\frac{1}{x}-\frac{2}{3}+\frac{1}{4}\right)\left(\frac{1}{x}-\frac{2}{3}-\frac{1}{4}\right)=0\)

\(\Leftrightarrow\left(\frac{1}{x}-\frac{5}{12}\right)\left(\frac{1}{x}-\frac{11}{12}\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}\frac{1}{x}-\frac{5}{12}=0\\\frac{1}{x}-\frac{11}{12}=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}\frac{1}{x}=\frac{5}{12}\\\frac{1}{x}=\frac{11}{12}\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{12}{11}\\x=\frac{12}{5}\end{cases}}\)

Vậy....

Answer 2

\(\left(\frac{1}{x}-\frac{2}{3}\right)^2-\frac{1}{16}=0\)

\(\Rightarrow\left(\frac{1}{x}-\frac{2}{3}\right)^2=\frac{1}{16}\)

\(\Rightarrow\left(\frac{1}{x}-\frac{2}{3}\right)^2=\left(\frac{1}{4}\right)^2\)

\(\Rightarrow\frac{1}{x}-\frac{2}{3}=\frac{1}{4}\)

\(\Rightarrow\frac{1}{x}=\frac{11}{12}\)

\(\Rightarrow x=\frac{11}{12}\)

Answer 3

\(=>\left(\frac{1}{x}-\frac{2}{4}\right)^2=\frac{1}{16}\)

=> \(\orbr{\begin{cases}\frac{1}{x}-\frac{2}{4}=\frac{1}{4}\\\frac{1}{x}-\frac{2}{4}=-\frac{1}{4}\end{cases}}\)

=>\(\orbr{\begin{cases}\frac{1}{x}=\frac{3}{4}\\\frac{1}{x}=\frac{1}{4}\end{cases}}\)

=> \(\orbr{\begin{cases}x=\frac{4}{3}\\x=4\end{cases}}\)

học tốt

Answer 4

cậu nghĩ tớ tin s ?

\(\left(\frac{1}{x}-\frac{2}{3}\right)^2-\frac{1}{16}=0\)

\(\left(\frac{1}{x}-\frac{2}{3}\right)^2=\left(\frac{1}{4}\right)^2\)

\(\Rightarrow\orbr{\begin{cases}\frac{1}{x}-\frac{2}{3}=\frac{1}{4}\\\frac{1}{x}-\frac{2}{3}=-\frac{1}{4}\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{12}{11}\\x=\frac{12}{5}\end{cases}}}\)

Answer 5

\(\left(\frac{1}{x}-\frac{2}{3}\right)^2-\frac{1}{16}=0\)

\(\Leftrightarrow\left(\frac{1}{x}-\frac{2}{3}\right)^2=\frac{1}{16}\)

\(\Leftrightarrow\orbr{\begin{cases}\frac{1}{x}-\frac{2}{3}=\frac{-1}{4}\\\frac{1}{x}-\frac{1}{3}=\frac{1}{4}\end{cases}\Leftrightarrow\orbr{\begin{cases}\frac{1}{x}=\frac{5}{12}\\\frac{1}{x}=\frac{7}{12}\end{cases}\Leftrightarrow}\orbr{\begin{cases}5x=12\\7x=12\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{12}{5}\\x=\frac{12}{7}\end{cases}}}\)