ΔABC vuông tại B, ta có: \(BC=\sqrt{AC^2-AB^2}=\sqrt{15^2-9^2}=12\left(cm\right)\)

Khi đó: 

\(sinA=\dfrac{BC}{AC}=\dfrac{12}{15}=\dfrac{4}{5}\)

\(cosA=\dfrac{AB}{AC}=\dfrac{9}{15}=\dfrac{3}{5}\)

\(tanA=\dfrac{BC}{AB}=\dfrac{12}{9}=\dfrac{4}{3}\)

\(cotA=\dfrac{AB}{bC}=\dfrac{9}{12}=\dfrac{3}{4}\)

⇔ \(|x+1|-\dfrac{2}{3}=\dfrac{8}{5} \)

⇔ \(|x+1|=\dfrac{34}{15} \)

⇒ \(\left[{}\begin{matrix}x=\dfrac{19}{15}\\x=-\dfrac{49}{15}\end{matrix}\right.\)

Ta có: \(\dfrac{2x}{3}=\dfrac{3y}{4}=\dfrac{4z}{3}\)

⇔ \(\dfrac{12x}{18}=\dfrac{12y}{16}=\dfrac{12z}{9} \)

Áp dụng t/c dtsbn, ta có:

\(\dfrac{12x}{18}=\dfrac{12y}{16}=\dfrac{12z}{9}=\dfrac{12(x+y+z)}{18+16+9}=\dfrac{12.49}{43}=\dfrac{588}{43}\)

⇒ \(\left\{{}\begin{matrix}x=\dfrac{882}{43}\\y=\dfrac{784}{43}\\z=\dfrac{441}{43}\end{matrix}\right.\)

a) ⇔ \(4x^2+4x-x-1=0\)

⇔ \(4x^2+3x-1=0\)

⇔ \(4x(x+1)-(x+1)=0\)

⇔ \((x+1)(4x-1)=0\)

⇒ \(\left[{}\begin{matrix}x=-1\\x=\dfrac{1}{4}\end{matrix}\right.\)

Vậy...

b) \(x^3-4x^2+4x=0\)

⇔ \(x^2(x-2)-2x(x-2)=0\)

⇔ \((x-2)(x^2-2x)=0\)

⇒ \(\left[{}\begin{matrix}x=2\\x=0\end{matrix}\right.\)

Vậy...

c) \(x^2-3x+2=0\)

⇔ \(x(x-2)-(x-2)=0\)

⇔ \((x-1)(x-2)=0\)

⇒ \(\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)

Vậy...

⇔ \(B=\dfrac{1}{\sqrt{3}}+\dfrac{\left(\sqrt{3}-1\right)\left(\sqrt{3}-1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}+\dfrac{2}{\sqrt{3}}-\dfrac{\sqrt{3}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}\)

⇔ \(B=\dfrac{\text{3}}{\sqrt{3}}+\dfrac{3-2\sqrt{3}+1}{3-1}-\sqrt{3}\)

⇔ \(B=\sqrt{3}+\dfrac{\text{4}-2\sqrt{3}}{\text{2}}-\sqrt{3}\)

⇔ \(B=\dfrac{2\left(2-\sqrt{3}\right)}{2}=2-\sqrt{3}\)

\((7-2x)^2=49-28x+4x^2=4x^2-28x+49=(2x-7)^2\)

Dzịt nó ở trong bình phương nên đổi chỗ đc mà

chuyển vế sang là thành \(-8(2x-7)^2 \) chứ ạ

\((2x-7)^3=8(7-2x)^2\)

⇔ \((2x-7)^3=8(2x-7)^2\)       (*)

\(TH1: (2x-7)^2=0\)

Khi đó: \(2x-7=0\)  ⇔ \(x=\dfrac{7}{2} \)

\(TH2:\left(2x-7\right)^2\ne0\) 

Khi đó: (*) ⇔ \(2x-7=8\) (chia 2 vế cho \((2x-7)^2\))

⇔ \(x=\dfrac{15}{2} \) 

Vậy \(x=\dfrac{15}{2}\); \(x=\dfrac{7}{2}\)

mk k thấy hình =(((