\(A=\dfrac{cota-tana}{tana+2\cdot cota}\)

\(=\dfrac{\dfrac{cosa}{sina}-\dfrac{sina}{cosa}}{\dfrac{sina}{cosa}+2\cdot\dfrac{cosa}{sina}}\)

\(=\dfrac{cos^2a-sin^2a}{sina\cdot cosa}:\dfrac{sin^2a+2\cdot cos^2a}{sina\cdot cosa}\)

\(=\dfrac{cos^2a-sin^2a}{sin^2a+2\cdot cos^2a}\)

\(=\dfrac{1-2\cdot sin^2a}{sin^2a+2\left(1-sin^2a\right)}\)

\(=\dfrac{1-2\cdot sin^2a}{-sin^2a+2}\)

\(=\dfrac{1-2\cdot\left(\dfrac{1}{3}\right)^2}{-\left(\dfrac{1}{3}\right)^2+2}=\dfrac{1-\dfrac{2}{9}}{-\dfrac{1}{9}+2}=\dfrac{7}{9}:\dfrac{17}{9}=\dfrac{7}{17}\)

\(\hept{\begin{cases}x+y=m\\x^2+y^2=n\end{cases}\Rightarrow x^2+2xy+y^2=m^2\Rightarrow xy=\frac{m^2-n}{2}}\)

P =\(x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)=m.\left(n-\frac{m^2-2}{2}\right)\)

\(=m.\frac{3n-m^2}{2}=\frac{3mn-m^3}{2}\)

Ai giúp e đi ak e cần găp

1

a) \(A=\frac{x+2}{x+3}-\frac{5}{x^2+x-6}+\frac{1}{2-x}\left(ĐK:x\ne-3;x\ne2\right)\)

\(=\frac{x+2}{x+3}-\frac{5}{\left(x-2\right)\left(x+3\right)}-\frac{1}{x-2}\)

\(=\frac{\left(x+2\right)\left(x-2\right)-5-\left(x+3\right)}{\left(x-2\right)\left(x+3\right)}\)

\(=\frac{x^2-4-5-x-3}{\left(x-2\right)\left(x+3\right)}=\frac{x^2-x-12}{\left(x-2\right)\left(x+3\right)}=\frac{\left(x-4\right)\left(x+3\right)}{\left(x-2\right)\left(x+3\right)}=\frac{x-4}{x-2}\)

Để \(A=-\frac{3}{4}\)

\(\Leftrightarrow\frac{x-4}{x-2}=-\frac{3}{4}\)

\(\Leftrightarrow4\left(x-4\right)=-3\left(x-2\right)\)

\(\Leftrightarrow4x-16=-3x+6\)

\(\Leftrightarrow7x=22\Leftrightarrow x=\frac{22}{7}\left(tm\right)\)

Vậy \(x=\frac{22}{7}\) thì \(A=-\frac{3}{4}\)

b) \(A=\frac{x-4}{x-2}=\frac{\left(x-2\right)-2}{x-2}=1-\frac{2}{x-2}\)

Để \(A\in Z\Rightarrow\frac{2}{x-2}\in Z\Rightarrow x-2\inƯ\left(2\right)\)

Mà: \(Ư\left(2\right)=\left\{1;-1;2;-2\right\}\)

=> \(x-2\in\left\{1;-1;2;-2\right\}\)

+) \(x-2=1\Rightarrow x=3\left(tm\right)\)

+) \(x-2=-1\Rightarrow x=1\left(tm\right)\)

+) \(x-2=2\Rightarrow x=4\left(tm\right)\)

+) \(x-2=-2\Rightarrow x=0\left(tm\right)\)

Vậy \(x\in\left\{0;1;3;4\right\}\) thì \(A\in Z\)

A=x+2/x+3-5/(x-2)(x+3)-1/x-2

A=(x+2)(x-2)-5-x-3/(x-2)(x+3)

A=x^2-4-5-x-3/(x-2)(x+3)

A=x^2-x-12/(x-2)(x+3)

A=(x+3)(x-4)/(x-2)(x+3)

A=x-4/x-2

Để A=-3/4 thì x-4/x-2=-3/4

Từ đó suy ra (x-4)4=-3(x-2)

4x-16=-3x+6

7x=22

x=22/7

b,Do A nguyên nên x-4/x-2 nguyên(x#2)

suy ra x-4-x+2 chia hết cho x-2

nên 2 chia hết cho x-2

mà ước 2=-2;-1;1;2

nên x=0;1;3;4

10.213

11. 2 giờ 55 phút

12. 4 ngày 21 giờ

13.

a: 6,008

b: 4500

c: 5,628

d: 4,009

mình ko hiểu ạ ở câu 1 và 2

=(4x0.25)x(2x0.5)

=1x1=1

ủa ko biết nữa ko biết nữa ko biết đáp án ở đâu

9999 / 36 - 15*11 = 1111 / 4 - 165 = 1111 / 4 - 660 / 4 = 451 / 4 = 112 ,75

\(A=1-1-\dfrac{5}{6}+1+\dfrac{7}{12}-1-\dfrac{9}{20}+1+\dfrac{11}{30}-1-\dfrac{13}{42}+1+\dfrac{15}{56}-1-\dfrac{17}{72}+1+\dfrac{19}{90}\)

\(=1-\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}+\dfrac{1}{4}-\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{9}+\dfrac{1}{10}\)

=1/2+1/10

=5/10+1/10=6/10=3/5