\(x=\frac{\left[6+3^2.2-6.3^2\right]^2}{\left[3^2+3.3^2-3^4\right]^2}=\frac{\left[6\left[1+3-9\right]\right]^2}{\left[9+27-81\right]^2}=\frac{\left[-30\right]^2}{\left[-45\right]^2}=\frac{900}{2025}=\frac{4}{9}\)

b) \(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=\frac{4^5.\left(1+1+1+1\right)}{3^5.\left(1+1+1\right)}.\frac{6^5.\left(1+1+1+1+1+1\right)}{2^5.\left(1+1\right)}\)

                                                                                                       \(=\frac{4^5.4}{3^5.3}.\frac{6^5.6}{2^5.2}=\frac{4^6}{3^6}.\frac{6^6}{2^6}=\frac{2^{12}.2^6.3^6}{3^6.2^6}=2^{12}\)

   Ta có: \(2^{12}=\left(2^3\right)^4=8^4\)                                                    

Vậy x= 4

\(x+3,5-\frac{4}{7}=\frac{3}{2}-5\frac{1}{8}\)

\(x+3,5-\frac{4}{7}=-\frac{29}{8}\)

\(x+3,5=-\frac{29}{8}+\frac{4}{7}\)

\(x+3,5=-\frac{117}{56}\)

      \(\Leftrightarrow x=-\frac{367}{56}\)

a)  \(=\frac{1}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}.\frac{5.5}{4.6}.\frac{6.6}{5.7}=\frac{6}{2.7}=\frac{3}{7}\)

B) \(=\frac{70}{11}+\frac{1}{9}-\frac{37}{11}-\frac{1}{9}=\left(\frac{70}{11}-\frac{37}{11}\right)+\left(\frac{1}{9}-\frac{1}{9}\right)=\frac{33}{11}+0=3\)

BÀI 2:

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

\(\Leftrightarrow\frac{7x-x+2x}{2}=\frac{35}{12}\)

\(\Leftrightarrow\frac{8x}{2}=\frac{35}{12}\)

\(\Leftrightarrow8x.12=35.2\Leftrightarrow96x=70\Leftrightarrow x=\frac{70}{96}=\frac{35}{48}\)

b) \(\left(x-\frac{3}{1.2}\right)+\left(x-\frac{3}{2.3}\right)+...+\left(x-\frac{3}{99.100}\right)=1\)

\(x-\frac{3}{1.2}+x-\frac{3}{2.3}+....x+\frac{3}{99.100}=1\)

\(\Leftrightarrow\left(x+x+x+...+x\right)-3\left(\frac{1}{1.2}+\frac{1}{1.3}+....+\frac{1}{99.100}\right)=1\)

ngoặc 1 có 99 số hạng x

\(\Leftrightarrow99x-3\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{99}-\frac{1}{100}\right)=1\)

\(\Leftrightarrow99x-3\left(1-\frac{1}{100}\right)=1\)

\(\Leftrightarrow99x-3.\frac{99}{100}=1\)

\(\Leftrightarrow99x=1+\frac{3.99}{100}\)

\(\Leftrightarrow99x=\frac{397}{100}\)

\(\Leftrightarrow x=\frac{397}{100.99}=\frac{397}{9900}\)

mk ko viết lại đề

\(A=\frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}+\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}+2^{12}.3^{12}}\)

\(=\frac{2^{12}.3^4\left(3-1\right)}{2^{12}.3^5\left(3+1\right)}+\frac{2^{12}.3^{10}\left(1+5\right)}{2.\left(2^{12}.3^{12}\right)}\)

\(=\frac{2}{3.4}+\frac{2^{12}.3^{10}.6}{2.2^{12}.3^{12}}=\frac{1}{6}+\frac{1}{3}=\frac{1}{2}\)

Vậy A= \(\frac{1}{2}\)

Bài 1:

\(\text{Giả sử: }\frac{x}{2}=\frac{y}{4}=\frac{z}{6}=k\)

\(\Rightarrow x=2k;y=4k;z=6k\)

Thay vào: x-y +z= 2k- 4k+ 6k= 8

                           = 4k= 8

=> k= \(\frac{8}{4}=2\)

=> x= 2. 2= 4

     y= 4. 2= 8

     z= 6.2 = 12

Vậy \(\begin{cases}x=4\\y=8\\z=12\end{cases}\)

Bài 2:

Giải:

Gọi số học sinh 4 khối 6, 7, 8, 9 là a, b, c, d ( a,b,c,d thuộc N* )

Ta có: \(\frac{a}{3}=\frac{b}{3,5}=\frac{c}{4,5}=\frac{d}{4}\) và a + b + c + d = 660

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\frac{a}{3}=\frac{b}{3,5}=\frac{c}{4,5}=\frac{d}{4}=\frac{a+b+c+d}{3+3,5+4,5+4}=\frac{660}{15}=44\)

+) \(\frac{a}{3}=44\Rightarrow a=132\)

+) \(\frac{b}{3,5}=44\Rightarrow b=154\)

+) \(\frac{c}{4,5}=44\Rightarrow c=198\)

+) \(\frac{d}{4}=44\Rightarrow d=176\)

Vậy khối 6 có 132 học sinh

        khối 7 có 154 học sinh

        khối 8 có 198 học sinh

        khối 9 có 176 học sinh

Bài 1:

Giải:

Áp dụng tính chất dãy tỉ số bằng nhau:

\(\frac{x}{2}=\frac{y}{4}=\frac{z}{6}=\frac{z-y+z}{2-4+6}=\frac{8}{4}=2\)

+) \(\frac{x}{2}=2\Rightarrow x=4\)

+) \(\frac{y}{4}=2\Rightarrow y=8\)

+) \(\frac{z}{6}=2\Rightarrow z=12\)

Vậy bộ số \(\left(x,y,z\right)\) là: \(\left(4,8,12\right)\)