\(x\left(x+1\right)=156\)
\(\Rightarrow x^2+x=156\)
\(\Rightarrow x^2+x-156=0\)
\(\Rightarrow x^2+13x-12x-156=0\)
\(\Rightarrow x\left(x+13\right)-12\left(x+13\right)=0\)
\(\Rightarrow\left(x+13\right)\left(x-12\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=12\\x=-13\end{matrix}\right.\)
___________________
\(x\left(x+1\right)=342\)
\(\Rightarrow x^2+x=342\)
\(\Rightarrow x^2+x-342=0\)
\(\Rightarrow x^2+19x-18x-342=0\)
\(\Rightarrow x\left(x+19\right)-18\left(x+19\right)=0\)
\(\Rightarrow\left(x+19\right)\left(x-18\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-19\\x=18\end{matrix}\right.\)
__________________
\(x\left(x+1\right)=650\)
\(\Rightarrow x^2+x=650\)
\(\Rightarrow x^2-x+650=0\)
\(\Rightarrow x^2+26x-25x-650=0\)
\(\Rightarrow x\left(x+26\right)-25\left(x+26\right)=0\)
\(\Rightarrow\left(x+26\right)\left(x-25\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-26\\x=25\end{matrix}\right.\)
______________________
\(x\left(x+1\right)=380\)
\(\Rightarrow x^2+x=380\)
\(\Rightarrow x^2+x-380=0\)
\(\Rightarrow x^2+20x-19x-380=0\)
\(\Rightarrow x\left(x+20\right)-19\left(x+20\right)=0\)
\(\Rightarrow\left(x+20\right)\left(x-19\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-20\\x=19\end{matrix}\right.\)
a, \(x\).(\(x\) + 1) = 156
156 = 22.3.13 = 12.13
Vậy \(x\).(\(x\) + 1) = 12.13
Vậy \(x\) = 12
b, \(x.\)(\(x\) + 1) = 342
342 = 2.32.19 = 18.19
\(x\).(\(x+1\)) = 18.19
\(x\) = 18
c, \(x\).(\(x\) + 1) = 650
650 = 2.52.13 = 25.26
\(x\).(\(x\) +1) = 25.26
\(x\) = 25
d, \(x\).(\(x\) +1) = 380
380 = 22.5.19 = 19.20
\(x\).(\(x\) + 1) = 19.20
\(x\) = 19