Ta có : \(\frac{x+2}{10^{10}}+\frac{x+2}{11^{11}}=\frac{x+2}{12^{12}}+\frac{x+2}{13^{13}}\)
=> \(\frac{x+2}{10^{10}}+\frac{x+2}{11^{11}}-\frac{x+2}{12^{12}}-\frac{x+2}{13^{13}}=0\)
=> \(\left(x+2\right)\left(\frac{1}{10^{10}}+\frac{1}{11^{11}}-\frac{1}{12^{12}}-\frac{1}{13^{13}}\right)=0\)
Vì \(\frac{1}{10^{10}}+\frac{1}{11^{11}}\ne\frac{1}{12^{12}}+\frac{1}{13^{13}}\) => \(\frac{1}{10^{10}}+\frac{1}{11^{11}}-\frac{1}{12^{12}}-\frac{1}{13^{13}}\ne0\)
=> \(x+2=0\)
=> \(x=-2\)
Ta có:
\(\frac{x+2}{10^{10}}+\frac{x+2}{11^{11}}=\frac{x+2}{12^{12}}+\frac{x+2}{13^{13}}\)\(\Rightarrow\left(x+2\right)\frac{1}{10^{10}}+\left(x+2\right)\frac{1}{11^{11}}=\left(x+2\right)\frac{1}{12^{12}}+\left(x+2\right)\frac{1}{13^{13}}\)
\(\Rightarrow\left(x+2\right)\left(\frac{1}{10^{10}}+\frac{1}{11^{11}}\right)=\left(x+2\right)\left(\frac{1}{12^{12}}+\frac{1}{13^{13}}\right)\)
Vì \(\frac{1}{10^{10}}+\frac{1}{11^{11}}\ne\frac{1}{12^{12}}+\frac{1}{13^{13}}\ne0\) nên \(x+2=0\Rightarrow x=-2\)
