Tìm x, biết: ( $x^{2}$ + 3)($x^{7}$ + 2) = 910 10/08/2021 Bởi Kinsley Tìm x, biết: ( $x^{2}$ + 3)($x^{7}$ + 2) = 910
Đáp án: x=2 Giải thích các bước giải: \(\begin{array}{l}\left( {{x^2} + 3} \right)\left( {{x^7} + 2} \right) = 910\\ \to {x^9} + 3{x^7} + 2{x^2} + 6 – 910 = 0\\ \to {x^9} + 3{x^7} + 2{x^2} – 904 = 0\\ \to {x^9} – 2{x^8} + 2{x^8} – 4{x^7} + 7{x^7} – 14{x^6} + 14{x^6} – 28{x^5} + 28{x^5} – 56{x^4}\\ + 56{x^4} – 112{x^3} + 112{x^3} – 224{x^2} + 226{x^2} – 452x + 452x – 904 = 0\\ \to {x^8}\left( {x – 2} \right) + 2{x^7}\left( {x – 2} \right) + 7{x^6}\left( {x – 2} \right) + 14{x^5}\left( {x – 2} \right) + 28{x^4}\left( {x – 2} \right)\\ + 56{x^3}\left( {x – 2} \right) + 112{x^2}\left( {x – 2} \right) + 226x\left( {x – 2} \right) + 452\left( {x – 2} \right) = 0\\ \to \left( {x – 2} \right)\left( {{x^8} + 2{x^7} + 7{x^6} + 14{x^5} + 28{x^4} + 56{x^3} + 112{x^2} + 226x + 452} \right) = 0\\ \to x – 2 = 0\\\left( {Do:{x^8} + 2{x^7} + 7{x^6} + 14{x^5} + 28{x^4} + 56{x^3} + 112{x^2} + 226x + 452 > 0\forall x} \right)\\ \to x = 2\end{array}\) Bình luận
Đáp án:
x=2
Giải thích các bước giải:
\(\begin{array}{l}
\left( {{x^2} + 3} \right)\left( {{x^7} + 2} \right) = 910\\
\to {x^9} + 3{x^7} + 2{x^2} + 6 – 910 = 0\\
\to {x^9} + 3{x^7} + 2{x^2} – 904 = 0\\
\to {x^9} – 2{x^8} + 2{x^8} – 4{x^7} + 7{x^7} – 14{x^6} + 14{x^6} – 28{x^5} + 28{x^5} – 56{x^4}\\
+ 56{x^4} – 112{x^3} + 112{x^3} – 224{x^2} + 226{x^2} – 452x + 452x – 904 = 0\\
\to {x^8}\left( {x – 2} \right) + 2{x^7}\left( {x – 2} \right) + 7{x^6}\left( {x – 2} \right) + 14{x^5}\left( {x – 2} \right) + 28{x^4}\left( {x – 2} \right)\\
+ 56{x^3}\left( {x – 2} \right) + 112{x^2}\left( {x – 2} \right) + 226x\left( {x – 2} \right) + 452\left( {x – 2} \right) = 0\\
\to \left( {x – 2} \right)\left( {{x^8} + 2{x^7} + 7{x^6} + 14{x^5} + 28{x^4} + 56{x^3} + 112{x^2} + 226x + 452} \right) = 0\\
\to x – 2 = 0\\
\left( {Do:{x^8} + 2{x^7} + 7{x^6} + 14{x^5} + 28{x^4} + 56{x^3} + 112{x^2} + 226x + 452 > 0\forall x} \right)\\
\to x = 2
\end{array}\)