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a. \(\frac{x+1}{2}=\frac{8}{x+1}\)
\(\Leftrightarrow\left(x+1\right).\left(x+1\right)=8.2\)
\(\Leftrightarrow\left(x+1\right)^2=16\)
\(\Leftrightarrow\left(x+1\right)^2=2^4\)
\(\Leftrightarrow\left(x+1\right)=2^2\)
\(\Leftrightarrow\left(x+1\right)=4\)
\(\Leftrightarrow x=4-1=3\)
b. \(x:\left(9\frac{1}{2}-\frac{3}{2}\right)=\frac{0,4+\frac{2}{9}-\frac{2}{11}}{1,6+\frac{8}{9}-\frac{8}{11}}\)
\(\Leftrightarrow x:\left(\frac{10}{2}-\frac{3}{2}\right)=\frac{0,4+0,2-0,18}{1,6+0,8-0,72}\)
\(\Leftrightarrow x:\frac{7}{2}=\frac{\frac{21}{50}}{\frac{42}{25}}\)
\(\Leftrightarrow x=\frac{\frac{21}{50}}{\frac{42}{25}}.\frac{7}{2}\Leftrightarrow x=\frac{1}{4}.\frac{7}{2}=\frac{7}{8}\)
a ) \(\frac{x+1}{2}=\frac{8}{x+1}\)
\(\Rightarrow\left(x+1\right).\left(x+1\right)=2.8\)
\(\Rightarrow\left(x+1\right)^2=16\)
\(\Rightarrow\orbr{\begin{cases}x+1=4\\x+1=-4\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=4-1\\x=-4-1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=3\\x=-5\end{cases}}\)
Dấu " \(\orbr{\begin{cases}\\\end{cases}}\)là hoặc nha !!!
\(\frac{x+1}{9}+\frac{x+2}{8}+\frac{x+3}{7}+...+\frac{x+9}{1}=-9\)
\(\left(\frac{x+1}{9}+1\right)+\left(\frac{x+2}{8}+1\right)+\left(\frac{x+3}{7}+1\right)+...+\left(\frac{x+9}{1}+1\right)=0\)
\(\frac{x+10}{9}+\frac{x+10}{8}+\frac{x+10}{7}+...+\frac{x+10}{1}=0\)
\(\left(x+10\right).\left(\frac{1}{9}+\frac{1}{8}+\frac{1}{7}+...+1\right)=0\)
vì \(\frac{1}{9}+\frac{1}{8}+\frac{1}{7}+...+1\ne0\)
\(\Rightarrow x+10=0\)
\(\Rightarrow x=-10\)
a ) (x+1)2=16
=>x+1=4 (vì x là số tự nhiên nên x+1=-4 là ko thỏa mãn)
=>x=3
b)x=2 ( cậu quy đồng rồi tự giải , có gì ko hiểu thì hỏi riêng mình )
\(x:\frac{1}{2}+x:\frac{1}{4}+x:\frac{1}{8}+..+x:\frac{1}{512}=x.2+x.4+x.8+...x.512=x\left(2+4+8+...+512\right)=...\)
Bài 1:
\(B=\frac{\frac{1}{2}+\frac{3}{4}-\frac{5}{6}}{\frac{1}{4}+\frac{3}{8}-\frac{5}{12}}+\frac{\frac{3}{4}+\frac{3}{5}-\frac{3}{8}}{\frac{1}{4}+\frac{1}{5}-\frac{1}{8}}\)\(=\frac{\frac{1}{2}+\frac{3}{4}-\frac{5}{6}}{\frac{1}{2}\left(\frac{1}{2}+\frac{3}{4}-\frac{5}{6}\right)}+\frac{3\left(\frac{1}{4}+\frac{1}{5}-\frac{1}{8}\right)}{\frac{1}{4}+\frac{1}{5}-\frac{1}{8}}\)
\(=\frac{1}{\frac{1}{2}}+3\) \(=2+3\) \(=5\)
Vậy B=5
Bài 2:
a) x3 - 36x = 0
=> x(x2-36)=0
=> x(x2+6x-6x-36)=0
=> x[x(x+6)-6(x+6) ]=0
=> x(x+6)(x-6)=0
\(\Rightarrow\orbr{\begin{cases}^{x=0}x+6=0\\x-6=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}^{x=0}x=-6\\x=6\end{cases}}\)
Vậy x=0; x=-6; x=6
b) (x - y = 4 => x=4+y)
x−3y−2 =32
=>2(x-3) = 3(y-2)
=>2x-6= 3y-6
=>2x-3y=0
=>2(4+y)-3y=0
=>8+2y-3y=0
=>8-y=0
=>y=8 (thỏa mãn)
Do đó x=4+y=4+8=12 (thỏa mãn)
Vậy x=12 và y =8
B= 1/2 + 3/4 - 5/6/1/2(1.2 + 3/4 - 5/6) + 3(1/4+ 1/5 - 1/8)/ 1/4 1/5 - 1/8
B= 1/ 1/2 + 3
B= 2+3
B=5
B2:
a) x^3 - 36x = 0
x(x^2 - 36) = 0
=> x=0 hoặc x^2-36=0
=> x= 0 hoặc x^2=36
=> x=0 hoặc x= +- 6
\(\frac{x+1}{2}=\frac{8}{x+1}\)
\(\Rightarrow\left(x+1\right)^2=16\)
\(\Rightarrow\orbr{\begin{cases}x+1=4\\x+1=-4\end{cases}}\Rightarrow\orbr{\begin{cases}x=3\\x=-5\end{cases}}\)
\(\frac{x+1}{2}=\frac{8}{x+1}\Rightarrow\left(x+1\right).\left(x+1\right)=2.8\)
\(\Rightarrow2\left(x+1\right)=16\Rightarrow x+1=8\Rightarrow x=7\)