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1+2+3+4+.....+x=45
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x+1 + x+2 + x+3 + x +4 + x+5 = 45
x + x + x + x + x = 45 -1 -2 -3 -4 -5
5x = 30
x =6
\(\frac{2}{3}x\frac{4}{y}=\frac{4}{45}:\frac{1}{5}\)\(=\frac{4}{15}\)
\(\frac{4}{y}=\frac{4}{15}:\frac{2}{3}\)\(=\frac{2}{5}\)
y=4:\(\frac{2}{5}\) y=10
\(\frac{3}{4}x\frac{y}{5}=\frac{15}{4}\)
\(\frac{y}{5}=\frac{15}{4}:\frac{3}{4}=5\)
y=5x5=25
a) \(1+2+...+x=45\)
\(\Rightarrow\frac{x\left(x+1\right)}{2}=45\)
\(\Rightarrow x\left(x+1\right)=90\)
\(\Rightarrow x\left(x+1\right)=9\cdot10\)
VẬy x = 9
\(a,\Leftrightarrow x-1=4\Leftrightarrow x=5\\ b,\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{3}{4}\\3x+1=4x-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{3}{4}\\x=4\left(tm\right)\end{matrix}\right.\Leftrightarrow x=4\\ c,ĐK:x\ge-5\\ PT\Leftrightarrow2\sqrt{x+5}-3\sqrt{x+5}+4\sqrt{x+5}=6\\ \Leftrightarrow3\sqrt{x+5}=6\\ \Leftrightarrow\sqrt{x+5}=3\\ \Leftrightarrow x+5=9\\ \Leftrightarrow x=4\left(tm\right)\)
\(d,\Leftrightarrow\sqrt{\left(x-2\right)^2}=\sqrt{\left(\sqrt{5}+1\right)^2}\\ \Leftrightarrow\left|x-2\right|=\sqrt{5}+1\\ \Leftrightarrow\left[{}\begin{matrix}x-2=\sqrt{5}+1\\2-x=\sqrt{5}+1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{5}+3\\x=1-\sqrt{5}\end{matrix}\right.\)
\(1+2+.......+x=45\)
\(\Rightarrow\frac{x\left(x+1\right)}{2}=45\)
\(\Rightarrow x\left(x+1\right)=90\)
mà \(90=9.10\)
\(\Rightarrow x=9\)
1 + 2 + 3 + 4 + ... + x = 45
(1 + x) × x : 2 = 45
(1 + x) × x = 45 × 2
(1 + x) × x = 90
(1 + x) × x = 10 × 9
=> x = 9
Vậy x = 9