Ta có \(\widehat{A^1}+\widehat{A^2}\) = 90⁰

\(\widehat{B}+\widehat{C}=90^0\); \(\widehat{A^1}+\widehat{C}=90^0\)

=> \(\widehat{A^1}=\widehat{B}\) ; \(\widehat{A^2}=\widehat{C}\)

Xét Δ ABH và ΔCAH có:  \(\widehat{A^1}=\widehat{B}\) ; \(\widehat{A^2}=\widehat{C}\)

=> Δ ABH ∼ ΔCAH (g.g)

=> \(\dfrac{BH}{AH}=\dfrac{AH}{CH}\) => AH² = BH.CH = 9 . 16 = 144

=> AH = 12

=> AB = \(\sqrt{BH^2+AH^2}\) = 15

=> AC = \(\sqrt{CH^2+AH^2}\) = 20

=> BC = 9 + 16 = 25

=> AB = 15;AC = 20;BC = 25

Ta có:

 1+2018+2018²+2018³+...+2018⁷ 

= (1+2018)+(2018²+2018³)+(2018⁴+2018⁵)+(2018⁶+2018⁷)

= (1+2018)+2018² (1+2018) +2018⁴ (1+2018)+2018⁶ (1+2018)

= (1+2018) ( 1+2018²+2018⁴+2018⁶)

= 2019 ( 1+2018²+2018⁴+2018⁶)  chia hết cho 9 (đpcm)

Học tốt

Hand@

2 A

3 D

4 A

5 A

6 B

7 A

8 A

9 A

ảnh lỗi

Bài này trong sách là trên mạng có ấy c lên ytb shears cho nhanh 

a: \(=\dfrac{x^3+2x+2x-2-x^2-x-1}{\left(x-1\right)\left(x^2+x+1\right)}\)

\(=\dfrac{x^3-x^2+3x-3}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x^2+3}{x^2+x+1}\)

b: \(=\dfrac{x^2-2x-3+x^2+2x-3+2x-2x^2}{\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{2x-6}{\left(x-3\right)\left(x+3\right)}=\dfrac{2}{x+3}\)

c: \(=\dfrac{6-7+x}{3\left(x-1\right)}=\dfrac{x-1}{3\left(x-1\right)}=\dfrac{1}{3}\)

d: \(=\dfrac{x^3+2x+2x-2-x^2-x-1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x^3-x^2+3x-3}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x^2+3}{x^2+x+1}\)