Question

tìm x biết

1+3+5+7+......+(2x+1) = 625

Answer 1

\(1+3+5+...+2x+1=625\)

\(\Rightarrow\left[\left(2x+1-1\right):2+1\right]\cdot\left(2x+1+1\right):2=625\)

\(\Rightarrow\left(2x:2+1\right)\cdot\left(2x+2\right):2=625\)

\(\Rightarrow\left(x+1\right)\cdot2\left(x+1\right):2=625\)

\(\Rightarrow\left(x+1\right)^2=625\)

\(\Rightarrow\left(x+1\right)^2=25^2\)

\(\Rightarrow\left[{}\begin{matrix}x+1=25\\x+1=-25\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=24\\x=-26\end{matrix}\right.\)