Google
Câu hỏi: Giá trị của biểu thức $P={{\left( 7+4\sqrt{3} \right)}^{2017}}.{{\left( 4\sqrt{3}-7 \right)}^{2016}}$ là
A. $P=1.$
B. $P=7-4\sqrt{3}.$
C. $P=7+4\sqrt{3}.$
D. $P=\dfrac{1}{3}.$
A. $P=1.$
B. $P=7-4\sqrt{3}.$
C. $P=7+4\sqrt{3}.$
D. $P=\dfrac{1}{3}.$
$P={{\left( 7+4\sqrt{3} \right)}^{2017}}{{\left( 4\sqrt{3}-7 \right)}^{2016}}=\left[ {{\left( 7+4\sqrt{3} \right)}^{2016}}.{{\left( 4\sqrt{3}-7 \right)}^{2016}} \right]\left( 7+4\sqrt{3} \right)$
$={{\left( -1 \right)}^{2016}}\left( 7+4\sqrt{3} \right)=7+4\sqrt{3}$
$={{\left( -1 \right)}^{2016}}\left( 7+4\sqrt{3} \right)=7+4\sqrt{3}$
Đáp án C.