Đáp án:
x=2
Giải thích các bước giải:
\(\begin{array}{l}
\left( {{x^2} + 3} \right)\left( {{x^7} + 2} \right) = 910\\
\to {x^9} + 3{x^7} + 2{x^2} + 6 - 910 = 0\\
\to {x^9} + 3{x^7} + 2{x^2} - 904 = 0\\
\to {x^9} - 2{x^8} + 2{x^8} - 4{x^7} + 7{x^7} - 14{x^6} + 14{x^6} - 28{x^5} + 28{x^5} - 56{x^4}\\
+ 56{x^4} - 112{x^3} + 112{x^3} - 224{x^2} + 226{x^2} - 452x + 452x - 904 = 0\\
\to {x^8}\left( {x - 2} \right) + 2{x^7}\left( {x - 2} \right) + 7{x^6}\left( {x - 2} \right) + 14{x^5}\left( {x - 2} \right) + 28{x^4}\left( {x - 2} \right)\\
+ 56{x^3}\left( {x - 2} \right) + 112{x^2}\left( {x - 2} \right) + 226x\left( {x - 2} \right) + 452\left( {x - 2} \right) = 0\\
\to \left( {x - 2} \right)\left( {{x^8} + 2{x^7} + 7{x^6} + 14{x^5} + 28{x^4} + 56{x^3} + 112{x^2} + 226x + 452} \right) = 0\\
\to x - 2 = 0\\
\left( {Do:{x^8} + 2{x^7} + 7{x^6} + 14{x^5} + 28{x^4} + 56{x^3} + 112{x^2} + 226x + 452 > 0\forall x} \right)\\
\to x = 2
\end{array}\)
