Toán Lớp 7: 1) Cho A=1+$3^{2}$ + $3^{4}$ +-..+$3^{2006}$ Tìm x, y $27^{263x}$ . $9^{5y}$ = 8A+1

Question

Toán Lớp 7:  1) Cho A=1+$3^{2}$ + $3^{4}$ +......+$3^{2006}$  Tìm x, y  $27^{263x}$  . $9^{5y}$ = 8A+1

landinhngoc97 · Answer

mik gửi nha

minhhaanh · Answer

$ textit{Giải đáp + Lời giải và giải thích chi tiết:}$ $A=1+3^2+3^4+...+3^{2006}$   $3^2A=3^2(1+3^2+3^4+...+3^{2006})$   $9A=3^2+3^4+3^6+...+3^{2008}$   $9A-A=(3^2+3^4+3^6+...+3^{2008})-(1+3^2+3^4+...+3^{2006})$   $8A=3^{2008}-1$   $&rArr;8A+1=3^{2008}-1+1$   $&rArr;27^{263x}.9^{5y}=3^{2008}$   $&rArr;(3^3)^{263x}.(3^2)^{5y}=3^{2008}$   $&rArr;3^{789x}.3^{10y}=3^{2008}$   $&rArr;3^{789x+10y}=3^{2008}$   $&rArr;789x+10y=2008$   $ text{C&oacute;}$ 10y vdots2   2008 vdots2   &rArr;789x vdots2   $ text{$&rArr;x$ chẵn}$   $ text{Nếu $x=0$}$   $789x+10y=2008$   $&hArr;780.0+10y=2008$   $&hArr;10y=2008$   y=2008/10=1004/5   $ text{Nếu $x=2$}$   $789x+10y=2008$   $&hArr;789.2+10y=2008$   $&hArr;1578+10y=2008$   $&hArr;10y=2008-1578=430$   $&hArr;y=430:10=43$   $ text{Nếu $x geq4$}$   $789x+10y geq789.4+10y=3156+10y>2008$ $ text{loại}$   $ text{Vậy}$ (x,y)=(2; 43);(0; 1004/5)