Bài 36 : [TEX]\left\{ log_{2}x - 3^y =15 \\ 3^y.log_{2}x= 2log_{2}x + 3^{y+1}[/TEX]
ĐK: x > 0
Đặt [TEX]u=log_2x,v=3^y > 0[/TEX]
[TEX]\Rightarrow \left{\begin{u-v=15}\\{uv=2u+3v}[/TEX]
[TEX]\Rightarrow v(v+15)=2(v+15)+3v \Leftrightarrow v^2-10v-30=0 \Leftrightarrow v=5+ \sqrt{55}(TM),v=5- \sqrt{55}(loai)[/TEX]
[TEX]\Rightarrow u=20+ \sqrt{55}[/TEX]
[TEX]\Rightarrow \left{\begin{log_2x=20+ \sqrt{55} \Leftrightarrow x=2^{20+ \sqrt{55}}}\\{3^y=5+ \sqrt{55} \Leftrightarrow y=log_3(5+ \sqrt{55})}[/TEX]
Vậy HPT có nghiệm (x;y) như trên