so sánh: C=3^10+1/3^9+1 và D=3^9+1/3^8+1 19/08/2021 Bởi Camila so sánh: C=3^10+1/3^9+1 và D=3^9+1/3^8+1
Ta có: $C = \dfrac{3^{10}+1}{3^9+1}$ $C : 3 = \dfrac{3^{10} + 1}{3^{10} + 3}$ $C : 3 = \dfrac{3^{10} + 3 – 2}{3^{10} + 3}$ $C : 3 =1 – \dfrac{2}{3^{10}+3}$ $D = \dfrac{3^{9}+1}{3^8+1}$ $D: 3 = \dfrac{3^{9} + 1}{3^{9} + 3}$ $D : 3 = \dfrac{3^{9} + 3 – 2}{3^{9} + 3}$ $D : 3 =1 – \dfrac{2}{3^{9}+3}$ Vì : $\dfrac{2}{3^{10} + 3} < \dfrac{2}{3^{9} + 3}$ $⇒ 1 – \dfrac{2}{3^{10}+3} > 1 – \dfrac{2}{3^{9}+3}$ $⇒ C>D$ Bình luận
Ta có:
$C = \dfrac{3^{10}+1}{3^9+1}$
$C : 3 = \dfrac{3^{10} + 1}{3^{10} + 3}$
$C : 3 = \dfrac{3^{10} + 3 – 2}{3^{10} + 3}$
$C : 3 =1 – \dfrac{2}{3^{10}+3}$
$D = \dfrac{3^{9}+1}{3^8+1}$
$D: 3 = \dfrac{3^{9} + 1}{3^{9} + 3}$
$D : 3 = \dfrac{3^{9} + 3 – 2}{3^{9} + 3}$
$D : 3 =1 – \dfrac{2}{3^{9}+3}$
Vì : $\dfrac{2}{3^{10} + 3} < \dfrac{2}{3^{9} + 3}$
$⇒ 1 – \dfrac{2}{3^{10}+3} > 1 – \dfrac{2}{3^{9}+3}$
$⇒ C>D$
Đáp án(trong hình nhé)
Bạn tham khảo nhé!!!