a) \(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+100\right)=5750\)
\(\Rightarrow\left(x+x+x+...+x\right)+\left(1+2+3+..+100\right)=5750\Rightarrow x.100+\left(100+1\right)\cdot100:2=5750\)\
\(\Rightarrow x.100+5050=5750\Rightarrow x.100=700\Rightarrow x=7\)
b) \(\frac{x+1}{2}=\frac{8}{x+1}\Rightarrow\left(x+1\right)\left(x+1\right)=2.8\)
\(\Rightarrow\left(x+1\right)^2=16\Rightarrow\left(x+1\right)^2=4^2\)
\(\Leftrightarrow x+1=4\Rightarrow x=3\)
1.\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+100\right)=5750\)
\(\Leftrightarrow\left(x+x+x+...+x\right)+\left(1+2+3+...+100\right)=5750\)
\(\Leftrightarrow100x+5050=5750\)
\(\Leftrightarrow100x=5750-5050=700\)
\(\Leftrightarrow x=700:100=7\)
2. \(\frac{x+1}{2}=\frac{8}{x+1}\)
\(\Leftrightarrow\left(x+1\right).\left(x+1\right)=8.2\)
\(\Leftrightarrow\left(x+1\right).\left(x+1\right)=16\)
\(\Leftrightarrow\left(x+1\right)^2=16\)
\(\Leftrightarrow\left(x+1\right)=16:2\)
\(\Leftrightarrow\left(x+1\right)=8\)
\(\Leftrightarrow x=8-1=7\)
Bạn sửa lại chỗ bài 2. Ở chỗ:
\(\left(x+1\right)^2=16\) và các chỗ sau chỗ đó thành:
\(\left(x+1\right)^2=16\)
\(\Leftrightarrow\left(x+1\right)^2=4^2\)
\(\Leftrightarrow x+1=4\)
\(\Leftrightarrow x=4-1=3\)
a) \(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...........+\left(x+100\right)=5750\)
\(\Rightarrow\left(x+x+x+x+.............+x\right)+\left(1+2+3+..........+100\right)=5750\)
\(\Rightarrow100x+5050=5750\)
\(\Rightarrow100x=700\)
\(\Rightarrow x=7\)
b) Có \(\frac{x+1}{2}=\frac{8}{x+1}\)
\(\Rightarrow\left(x+1\right)\left(x+1\right)=2.8\)
\(\Rightarrow\left(x+1\right)^2=16\)
\(\Rightarrow\left(x+1\right)^2=4^2\)
\(\Rightarrow x+1=4\)
\(\Rightarrow x=4-1=3\)