Bài 7:

a: \(A=x+\sqrt{x}\ge0\forall x\)

Dấu '=' xảy ra khi x=0

16. how

17. how

18. which

19. What

20. whose

Bài 5: 

a: Xét ΔBEC và ΔADC có 

\(\widehat{C}\) chung

\(\widehat{EBC}=\widehat{DAC}\)

Do đó: ΔBEC\(\sim\)ΔADC

a) ĐKXĐ: \(\left\{{}\begin{matrix}x\le-1\\x\ge2\end{matrix}\right.\)

\(\sqrt{x^2-x-2}-\sqrt{x-2}=0\\ \Leftrightarrow\sqrt{x^2-x-2}=\sqrt{x-2}\\ \Leftrightarrow x^2-x-2=x-2\\ \Leftrightarrow x^2-2x=0\\ \Leftrightarrow x\left(x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\left(ktm\right)\\x=2\left(tm\right)\end{matrix}\right.\)

\(a,ĐK:x\ge2\\ PT\Leftrightarrow x^2-x-2=x-2\\ \Leftrightarrow x^2-2x=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\left(tm\right)\\x=0\left(ktm\right)\end{matrix}\right.\Leftrightarrow x=2\\ b,ĐK:\left[{}\begin{matrix}x\le-1\\x\ge1\end{matrix}\right.\\ PT\Leftrightarrow\sqrt{x^2-1}=x^2-1\\ \Leftrightarrow x^2-1=\left(x^2-1\right)^2\\ \Leftrightarrow\left(x^2-1\right)\left(x^2-1-1\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\left(tm\right)\\x=-1\left(tm\right)\\x=\sqrt{2}\left(tm\right)\\x=-\sqrt{2}\left(tm\right)\end{matrix}\right.\)

\(c,ĐK:\left[{}\begin{matrix}x\le-2\\x\ge1\end{matrix}\right.\\ PT\Leftrightarrow\sqrt{x^2-x}=-\sqrt{x^2+x-2}\\ \Leftrightarrow x^2-x=x^2+x-2\\ \Leftrightarrow2x=2\\ \Leftrightarrow x=1\left(tm\right)\)

a: tan B=2

=>\(\frac{\sin B}{cosB}=2\)

=>sin B=2*cosB

\(A=\frac{\sin B+cosB}{\sin B-cosB}\)

\(=\frac{2\cdot cosB+cosB}{2\cdot cosB-cosB}=\frac{3\cdot cosB}{cosB}=3\)

b: \(C=\sin^2a+2\cdot\sin a\cdot cosa-3\cdot cos^2a\)

\(=\left(\sin^2a+2\cdot\sin a\cdot cosa+cos^2a\right)-4\cdot cos^2a\)

\(=\left(\sin a+cosa\right)^2-4\cdot cos^2a=\left(3\cdot cosa\right)^2-4\cdot cos^2a=5\cdot cos^2a\)

c: \(D=\frac{\sin^2a-\sin a\cdot cosa-cos^2a}{2\cdot\sin a\cdot cosa}\)

\(=\frac{\left(2\cdot cosa\right)^2-2\cdot cosa\cdot cosa-cos^2a}{2\cdot2\cdot cosa\cdot cosa}\)

\(=\frac{4\cdot cos^2a-3\cdot cos^2a}{4\cdot cos^2a}=\frac{4-3}{4}=\frac14\)

a. Ý nghĩa:

Hiệu điện thế định mức của bóng đèn là 120V

Công suất định mức của bóng đèn là 60W

b. \(\left\{{}\begin{matrix}P=\dfrac{U^2}{R}\Rightarrow R=\dfrac{U^2}{P}=\dfrac{120^2}{60}=240\Omega\\P=UI\Rightarrow I=\dfrac{P}{U}=0,5A\end{matrix}\right.\)

c. \(U_b=U_m-U=220-120=100V\left(R_bntR\right)\)

\(I_m=I=I_b=0,5A\)

\(\Rightarrow R_b=\dfrac{U_b}{I_b}=\dfrac{100}{0,5}=200\Omega\)

d. \(R_{d_2}=\dfrac{U_{d_2}^2}{P_{d_2}}=\dfrac{120^2}{55}\approx261,8\Omega\)

\(I_m'=\dfrac{U_m'}{R_m'}=\dfrac{220}{240+261,8}\approx0,4A\)

\(\Rightarrow P_m'=U_m'\cdot I_m'=220\cdot0,4=88\)W

6) \(\left(2x+\dfrac{1}{2}\right)^3=8x^3+4x^2+\dfrac{3}{2}x+\dfrac{1}{8}\)

7) \(\left(x-3\right)^3=x^3-9x^2+27x-27\)

7: \(\left(x-3\right)^3=x^3-9x^2+27x-27\)