Theo đề bài ta có :
\(7^{2x}+7^{2x+2}=2450\)
\(\Rightarrow7^{2x}.\left(1+7^2\right)=2450\)
\(\Rightarrow7^{2x}.50=2450\)
\(\Rightarrow7^{2x}=2450:50\)
\(\Rightarrow7^{2x}=49\)
\(\Rightarrow7^{2x}=7^2\)
\(\Rightarrow2x=2\)
\(\Rightarrow x=2:2\)
\(\Rightarrow x=1\)
Vậy \(x=1\)