\(\frac{x^2-10x-29}{1971}+\frac{x^2-10x-27}{1972}=\frac{x^2-10x-1971}{29}+\frac{x^2-10x-1973}{27}\)
\(\Leftrightarrow\frac{x^2-10x-29}{1971}-1+\frac{x^2-10x-27}{1973}-1=\frac{x^2-10x-1971}{29}+\frac{x^2-10x-1973}{27}-1\)
\(\Leftrightarrow\frac{x^2-10x-29-1971}{1971}+\frac{x^2-10x-27-1973}{1973}=\frac{x^2-10x-1971-29}{29}+\frac{x^2-10x-1973-27}{27}\)
\(\Leftrightarrow\frac{x^2-10x-2000}{1971}+\frac{x^2-10x-2000}{1973}-\frac{x^2-10x-2000}{29}-\frac{x^2-10x-2000}{27}=0\)
\(\Leftrightarrow\left(x^2-10x-2000\right)\left(\frac{1}{1971}+\frac{1}{1973}-\frac{1}{29}-\frac{1}{27}\right)=0\)
\(\Leftrightarrow x^2-10x-2000=0\)
\(\Leftrightarrow x^2-50x+40x-2000=0\)
\(\Leftrightarrow x\left(x-50\right)+40\left(x-50\right)=0\)
\(\Leftrightarrow\left(x-50\right)\left(x+40\right)=0\)
Th1: \(x-50=0\Leftrightarrow x=50\)
Th2: \(x+40=0\Leftrightarrow x=-40\)
Vậy tập nghiệm của phương trình là \(S=\left\{50;-40\right\}\)