Question

Cho 144²⁰¹⁵ = 2^X x 3^Y. Tính \(\left(\frac{X+Y}{X-Y}\right)^{\frac{x}{y}}\)

Answer 1

\(144^{2015}=\left(2^4.3^2\right)^{2015}=2^{4.2015}.3^{2.2015}\)

\(\Rightarrow\left\{{}\begin{matrix}X=4.2015\\Y=2.2015\end{matrix}\right.\)

\(\left(\frac{X+Y}{X-Y}\right)^{\frac{X}{Y}}=\left(\frac{4.2015+2.2015}{4.2015-2.2015}\right)^{\frac{4.2015}{2.2015}}=\left[\frac{2015\left(4-2\right)}{2015\left(4+2\right)}\right]^{\frac{4}{2}}=\left(\frac{2}{6}\right)^2=\left(\frac{1}{3}\right)^2=\frac{1}{9}\)