Question

Tìm x biết: (12/25)^x =(3/5)² - (-3/5)⁴

Answer 1

\(\left(\dfrac{12}{25}\right)^X=\left(\dfrac{3}{5}\right)^2-\left(\dfrac{-3}{5}\right)^4\)

\(\left(\dfrac{12}{25}\right)^x=\dfrac{9}{25}-\dfrac{81}{625}\)

\(\left(\dfrac{12}{25}\right)^x=\dfrac{144}{625}\)

\(=>x=2\)

Answer 2

\(\left(\dfrac{12}{25}\right)^x=\left(\dfrac{3}{5}\right)^2-\left(-\dfrac{3}{5}\right)^4\)

\(\Leftrightarrow\left(\dfrac{12}{25}\right)^x=\left(\dfrac{3}{5}\right)^2-\left(\dfrac{3}{5}\right)^4\)

\(\Leftrightarrow\left(\dfrac{12}{25}\right)^x=\left(\dfrac{3}{5}\right)^2-\left(\dfrac{3}{5}\right)^2.\left(\dfrac{3}{5}\right)^2\)

\(\Leftrightarrow\left(\dfrac{12}{25}\right)^x=\left(\dfrac{3}{5}\right)^2.\left[1-\left(\dfrac{3}{5}\right)^2\right]\)

\(\Leftrightarrow\left(\dfrac{12}{25}\right)^x=\dfrac{144}{625}\)

\(\Leftrightarrow\left(\dfrac{12}{25}\right)^x=\left(\dfrac{12}{25}\right)^2\)

\(\Leftrightarrow x=2\)