Question

Tìm x,y biết: (2^x +1)(2^x +2) - 3^y =89

Answer 1

\(\Rightarrow2^{2x}+2^x+2\cdot2^x+2-3^y=89\Rightarrow4^x+3\cdot2^x+2-3^y=89\)

Ta thấy \(4\equiv1\left(mod3\right)\Rightarrow4^x\equiv1^x\equiv1\left(mod3\right);3\cdot2^x\equiv0\left(mod3\right);3^y\equiv0\left(mod3\right);2\equiv2\left(mod3\right)\Rightarrow4^x+3\cdot2^x-3^y+2\equiv1+0-0+2\equiv3\equiv0\left(mod3\right)\) Mà \(89\equiv2\left(mod3\right)\) \(\Rightarrow VT\ne VP\Rightarrow\)vô lí\(\Rightarrow\) ko tồn tại x,y Vậy...