Question

\(\dfrac{x^2-10x-29}{1971}+\dfrac{x^2-100-27}{1973}=\dfrac{x^2-10x-1971}{29}+\dfrac{x^2-10x-1973}{27}\)

Answer 1

`(x^2-10x-29)/1971+(x^2-10x-27)/1973=(x^2-10x-1971)/1929+(x^2-10x-1973)/1927`

`<=>(x^2-10x-29)/1971-1+(x^2-10x-27)/1973-1=(x^2-10x-1971)/1929-1+(x^2-10x-1973)/1927-1`

`<=>(x^2-10x-200)/1971+(x^2-10x-200)/1973=(x^2-10x-200)/1971+(x^2-10x-200)/1927`

`<=>(x^2-10x-200)(1/1971+1/1973-1/1929-1/1927)=0`

`<=>x^2-10x-200=0` do `1/1971+1/1973-1/1929-1/1927<0`

`<=>x^2-20x+10x-200=0`

`<=>x(x-20)+10(x-20)=0`

`<=>(x-20)(x+10)=0`

`<=>` \(\left[ \begin{array}{l}x=20\\x=-10\end{array} \right.\) 

Vậy `S={20,-10}`