a ) \(\left(4x+5\right)\div3-121\div11=4\)
\(\left(4x+5\right)\div3-11=4\)
\(\left(4x+5\right)\div3=4+11\)
\(\left(4x+5\right)\div3=15\)
\(\left(4x+5\right)=15\cdot3\)
\(4x+5=45\)
\(4x=45-5\)
\(4x=40\)
\(x=10\)
(4x + 5) : 3 - 121 : 11 = 4
=> (4x + 5) : 3 - 11 = 4
=> (4x + 5) : 3 = 15
=> 4x + 5 = 45
=> 4x = 40
=> x = 10
b) 1 + 3 + 5 + ... + x = 1600
=>[(x - 1) : 2 + 1] . (x + 1) : 2 = 1600
=> \(\left(\frac{x}{2}-\frac{1}{2}+1\right).\frac{x+1}{2}=1600\)
=> \(\frac{x+1}{2}.\frac{x+1}{2}=1600\)
=> \(\left(\frac{x+1}{2}\right)^2=1600\)
=> \(\frac{x+1}{2}=40\)
=> x + 1 = 80
=> x = 79
a,\(\left(4x+5\right):3-121:11=4\)
\(< =>\frac{4x+5}{3}-11=4\)
\(< =>\frac{4x+5}{3}=4+11=15\)
\(< =>4x+5=15.3=45\)
\(< =>4x=45-5=40< =>x=10\)
b, \(1+3+5+...+x=1600\)
Số số hạng : \(\left(x-1\right):2+1\)
Tổng : \(\frac{\left(x+1\right)\left(\frac{x-1}{2}+1\right)}{2}=\frac{\left(x+1\right)\left(\frac{x+1}{2}\right)}{2}=1600\)
\(< =>\frac{\left(x+1\right)^2}{2}=1600.2=3200\)
\(< =>\left(x+1\right)^2=3200.2=6400\)
\(< =>\left(x+1\right)^2=80^2=\left(-80\right)^2\)
\(< =>\orbr{\begin{cases}x+1=80\\x+1=-80\end{cases}< =>\orbr{\begin{cases}x=79\left(thoa-man\right)\\x=-81\left(loai\right)\end{cases}}}\)(do x > 0)
b ) \(1+3+5+...+x=1600\)
\(\left(x+1\right)\left[\left(\frac{x-1}{2}\right)+1\right]\div2=1600\)
\(\left(x+1\right)\left[\left(\frac{x-1}{2}\right)+1\right]=3200\)
\(\left(x+1\right)\left(\frac{x-1}{2}+\frac{2}{2}\right)=3200\)
\(\left(x+1\right)\left(\frac{x+1}{2}\right)=3200\)
\(\left(x+1\right)^2=6400\)
\(\left(x+1\right)^2=80^2\)
\(x+1=80\)
\(x=79\)
Bài giải
\(a,\text{ }\left(4x+5\right)\text{ : }3-121\text{ : }11=4\)
\(\left(4x+5\right)\text{ : }3-11=4\)
\(\left(4x+5\right)\text{ : }3=15\)
\(4x+5=45\)
\(4x=40\)
\(x=10\)
\(b,\text{ }1+3+5+...+x=1600\)
\(\left[\left(x-1\right)\text{ : }2+1\right]\left(x+1\right)\text{ : }2=1600\)
\(\left(\frac{x}{2}-\frac{1}{2}+1\right)\frac{\left(x+1\right)}{2}=1600\)
\(\frac{x+1}{2}\cdot\frac{x+1}{2}=800\)
\(\left(\frac{x+1}{2}\right)^2=800\)
\(\frac{x+1}{2}=40\)
\(x+1=80\)
\(x=79\)
a) \(\left(4x+5\right)\div3-121\div11=4\)
\(\left(4x+5\right)\div3-11=4\)
\(\left(4x+5\right)\div3=4+11\)
\(\left(4x+5\right)\div3=15\)
\(4x+5=15.3\)
\(4x+5=45\)
\(4x=45-5\)
\(4x=40\)
\(x=40\div4\)
\(x=10\)
b) \(1+3+5+...+x=1600\)
\(\left(x+1\right).\left[\left(x-1\right)\div2+1\right]\div2=1600\)
\(\left(x+1\right).\left[x\div2-1\div2+1\right]\div2=1600\)
\(\left(x+1\right).\left[\frac{x}{2}-\frac{1}{2}+\frac{2}{2}\right]\div2=1600\)
\(\left(x+1\right).\frac{x-1+2}{2}\div2=1600\)
\(\left(x+1\right).\frac{x+1}{2}.\frac{1}{2}=1600\)
\(\frac{\left(x+1\right).\left(x+1\right)}{2.2}=1600\)
\(\frac{\left(x+1\right)^2}{4}=1600\)
\(\left(x+1\right)^2=1600.4\)
\(\left(x+1\right)^2=6400\)
\(\left(x+1\right)^2=80^2\)
\(\Rightarrow x+1=80\)
\(\Rightarrow x=79\)