Ta có: \(\frac{x+2}{3}=\frac{y-1}{4}=\frac{z+5}{7}\)

\(\Rightarrow\frac{2\left(x+2\right)}{6}=\frac{y-1}{4}=\frac{z+5}{7}\)

\(\Rightarrow\frac{2x+4}{6}=\frac{y-1}{4}=\frac{z+5}{7}\)

Áp dụng tính chất dãy tỉ số bằng nhau được:

\(\frac{2x+4-\left(y-1\right)+z+5}{6-4+7}=\frac{2x+4-y+1+z+5}{6-4+7}=\frac{\left(2x-y+z\right)+\left(4+1+5\right)}{6-4+7}\)

                                                                                                     \(=\frac{17+10}{9}=\frac{27}{9}=3\)

Suy ra: \(2x+4=6.3\Rightarrow2x=14\Rightarrow x=7\)

            \(y-1=3.4\Rightarrow y=13\)

             \(z+5=3.7\Rightarrow z=16\)

Vậy x = 7 ; y = 13; z = 16

\(\frac{x-2}{x+6}=\frac{5}{7}\)

\(\Leftrightarrow\frac{5}{7}.\left(x+6\right)=x-2\)

\(\Leftrightarrow\frac{5}{7}x+\frac{30}{7}=x-2\)

\(\Leftrightarrow\frac{5}{7}x-x=-2-\frac{30}{7}\)

\(\Leftrightarrow-\frac{2}{7}x=-\frac{44}{7}\)

\(\Leftrightarrow x=-\frac{44}{7}:\left(-\frac{2}{7}\right)\)

\(\Leftrightarrow x=\frac{44}{7}.\frac{7}{2}=22\)

\(\frac{x-2}{x+6}=\frac{5}{7}\)

\(\Leftrightarrow7\left(x-2\right)=5\left(x+6\right)\)

\(\Rightarrow7x-14=5x+30\)

\(\Rightarrow7x-5x=14+30\)

\(\Rightarrow2x=44\)

\(\Rightarrow x=44:2=22\).

Chúc bạn học tốt ! Thanks !

\(2^x:1+2^x:2+...+2^x:49=2^{49}-1\)

\(2^x.1+2^x.\frac{1}{2}+...+2^x.\frac{1}{49}=2^{49}-1\)

\(2^x.\left(1+\frac{1}{2}+...+\frac{1}{49}\right)=2^{49}-1\)

Đặt: \(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{49}}\)

=> \(2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{48}}\)

=> \(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{48}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^{49}}\right)\)

=> \(A=1-\frac{1}{2^{49}}=\frac{2^{49}-1}{2^{49}}\)

\(2^{x-1}+2^{x-2}+2^{x-3}+...+2^{x-49}=2^{49}-1\)

<=> \(\frac{2^x}{2}+\frac{2^x}{2^2}+\frac{2^x}{2^3}+...+\frac{2^x}{2^{49}}=2^{49}-1\)

<=> \(2^x\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{49}}\right)=2^{49}-1\)

<=> \(2^x.\frac{2^{49}-1}{2^{49}}=2^{49}-1\)

<=> \(2^x=2^{49}\)

<=> x = 49.

\(\left(4x-1\right)^3=\frac{-1}{27}\)

\(\Rightarrow\left(4x-1\right)^3=\left(\frac{-1}{3}\right)^3\)

\(\Rightarrow4x-1=\frac{-1}{3}\)

\(\Rightarrow4x=\frac{-1}{3}+1\)

\(\Rightarrow4x=\frac{2}{3}\)

\(\Rightarrow x=\frac{2}{3}:4\)

\(\Rightarrow x=\frac{1}{6}\)

\(\frac{x}{4}=\frac{y}{7}=\frac{z}{9}\Leftrightarrow\frac{2x}{8}=\frac{y}{7}=\frac{2x-y}{8-7}=\frac{2}{1}=2\)

\(\Rightarrow\frac{x}{4}=2\Rightarrow x=8\)

\(\frac{y}{7}=2\Rightarrow y=14\)

\(\frac{z}{9}=2\Rightarrow z=18\)

=.= hok tốt!!

Sao x/4=y/7=z/9 suy ra 2x/8 = y/7 vậy Myyano Shiiho

Đây!

Từ \(\frac{x}{4}=\frac{y}{7}=\frac{z}{9}\)

ta có:\(\frac{x}{4}=\frac{y}{7}\)

\(\Rightarrow\frac{2x}{8}=\frac{y}{7}\)(nhân cả tử và mẫu của x/4 vs 2)