5/8

3/4

\(a)\dfrac{3}{4}.\dfrac{5}{6}=\dfrac{5}{8}\)

\(b)\dfrac{2}{7}:\dfrac{4}{9}=\dfrac{9}{14}\)

\(\dfrac{3}{4}x\dfrac{5}{6}=\dfrac{3x5}{4x6}=\dfrac{15}{24}=\dfrac{5}{8}\)

b) \(\dfrac{2}{7}:\dfrac{4}{9}=\dfrac{2}{7}x\dfrac{9}{4}=\dfrac{18}{28}=\dfrac{9}{14}\)

\(\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-4}}=2\sqrt{2}\)

\(\Leftrightarrow\sqrt{x+2\sqrt{2\left(x-2\right)}}+\sqrt{x-2\sqrt{2\left(x-2\right)}}=2\sqrt{2}\)

\(\Leftrightarrow2x+2\sqrt{\left[x+2\sqrt{2\left(x-2\right)}\text{ }\right]\left[x-2\sqrt{2\left(x-2\right)}\text{ }\right]}=8\)

\(\Leftrightarrow2\sqrt{\left[x+2\sqrt{2\left(x-2\right)}\text{ }\right]\left[x-2\sqrt{2\left(x-2\right)}\text{ }\right]}=8-2x\)

\(\Leftrightarrow4\left[x+2\sqrt{2\left(x-2\right)}\text{ }\right]\left[x-2\sqrt{2\left(x-2\right)}\text{ }\right]=64-32x+4x^2\)

\(\Leftrightarrow4x^2-32x+64=64-32x+4x^2+\)

\(\Leftrightarrow64=64\) (Đúng)

⇒ Phương trình có vô số nghiệm.

Vậy \(S=\mathbb R\).

\(\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-4}}=2\sqrt{2}\)

ĐK: \(x\ge2\), PT tương đương với:

\(x+2\sqrt{2x-4}+2\sqrt{\left(x+2\sqrt{2x-4}\right)\left(x-2\sqrt{2x-4}\right)}+x-2\sqrt{2x-4}=8\)

\(\Leftrightarrow2x+2\sqrt{x^2-4\left(2x-4\right)}=8\)

\(\Leftrightarrow2x+2\sqrt{x^2-8x+16}=8\\ \Leftrightarrow x+\left|x-4\right|=8\)

Với x < 4 => \(x+4-x=8\)

\(\Leftrightarrow4=8\) (loại)

Với \(x\ge4\) => \(x+x-4=8\)

\(\Leftrightarrow x=6\) (thỏa mãn)

Chỉ thấy bài 5 với 6:

5.

\(f'\left(x\right)+2f\left(x\right)=0\Leftrightarrow f'\left(x\right)=-2f\left(x\right)\Leftrightarrow\dfrac{f'\left(x\right)}{f\left(x\right)}=-2\)

Lấy nguyên hàm 2 vế:

\(\int\dfrac{f'\left(x\right)}{f\left(x\right)}dx=\int-2dx\Rightarrow ln\left(f\left(x\right)\right)=-2x+C\)

Thay \(x=1\Rightarrow0=-2+C\Rightarrow C=2\)

\(\Rightarrow ln\left(f\left(x\right)\right)=-2x+2\Rightarrow f\left(x\right)=e^{-2x+2}\)

\(\Rightarrow f\left(-1\right)=e^4\)

6.

\(f\left(x\right)+x.f'\left(x\right)=2x+1\)

\(\Leftrightarrow x'.f\left(x\right)+x.f'\left(x\right)=2x+1\)

\(\Leftrightarrow\left[x.f\left(x\right)\right]'=2x+1\)

Lấy nguyên hàm 2 vế:

\(\int\left[x.f\left(x\right)\right]'dx=\int\left(2x+1\right)dx\)

\(\Rightarrow x.f\left(x\right)=x^2+x+C\)

Thay \(x=1\Rightarrow1.f\left(1\right)=1+1+C\Rightarrow C=1\)

\(\Rightarrow f\left(x\right)=\dfrac{x^2+x+1}{x}\)

\(\Rightarrow f\left(2\right)=\dfrac{7}{2}\)

Ủa sao đề khác rồi:

3.

\(f'\left(x\right)=-e^x.f^2\left(x\right)\Leftrightarrow\dfrac{f'\left(x\right)}{f^2\left(x\right)}=-e^x\)

Lấy nguyên hàm 2 vế:

\(\int\dfrac{f'\left(x\right)}{f^2\left(x\right)}dx=\int-e^xdx\)

\(\Rightarrow\dfrac{1}{f\left(x\right)}=e^x+C\)

Thay \(x=0\Rightarrow2=1+C\Rightarrow C=1\)

\(\Rightarrow\dfrac{1}{f\left(x\right)}=e^x+1\Rightarrow f\left(x\right)=\dfrac{1}{e^x+1}\)

\(\Rightarrow f\left(ln2\right)=\dfrac{1}{3}\)

tháng 2 có 28 ngày

tháng 2 năm nhuận có 29 ngày

29 ngày

bạn ,bạn có nghĩ bạn đang sống ở nơi 1 tuần có 8 ngày ko

1/9

\(\dfrac{1}{2}\times\dfrac{2}{3}\times\dfrac{3}{4}\times\dfrac{4}{5}\times\dfrac{5}{6}\times\dfrac{6}{7}\times\dfrac{7}{8}\times\dfrac{8}{9}\)

\(=\dfrac{1\times2\times3\times4\times5\times6\times7\times8}{2\times3\times4\times5\times6\times7\times8\times9}\)

\(=\dfrac{1}{9}\)

1/9

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

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

\(P=\sqrt{2x+\sqrt{4x-1}}+\sqrt{2x-\sqrt{4x-1}}\) với \(\dfrac{1}{4}< x< \dfrac{1}{2}\)

\(\Leftrightarrow\sqrt{2}P=\sqrt{4x+2\sqrt{4x-1}}+\sqrt{4x-2\sqrt{4x-1}}\)

\(=\sqrt{\left(\sqrt{4x-1}\right)^2+2\sqrt{4x-1}+1}+\sqrt{\left(\sqrt{4x-1}\right)^2-2\sqrt{4x-1}+1}\)

\(=\sqrt{4x-1}+1+\left|\sqrt{4x-1}-1\right|\)

Do \(\dfrac{1}{4}< x< \dfrac{1}{2}\Leftrightarrow0< \sqrt{4x-1}< 1\)

\(\Rightarrow P=\dfrac{1}{\sqrt{2}}\left(\sqrt{4x-1}+1+1-\sqrt{4x-1}\right)=\sqrt{2}\)

Vậy \(P=\sqrt{2}\).

\(\left(\dfrac{2}{5}-\dfrac{1}{4}\right):\dfrac{3}{4}x\dfrac{5}{2}=\dfrac{3}{20}:\dfrac{3}{4}x\dfrac{5}{2}=\dfrac{3}{20}x\dfrac{4}{3}x\dfrac{5}{2}=\dfrac{3x4x5}{20x3x2}=\dfrac{1}{2}\)

`( 2 / 5 - 1 / 4 ) : 3 / 4 xx 5 / 2`

`=( 8 / 20 - 5 / 20 ) xx 4 / 3 xx 5 / 2`

`= 3 / 20 xx 4 / 3 xx 5 / 2`

`= [ 3 xx 4 xx 5 ] / [ 4 xx 5 xx 3 xx 2 ]`

`= 1 / 2`

(2/5 - 1/4) : 3/4 x 5/2
= 3/20 : 3/4 x 5/2
= 3/20 x 4/3 x 5/2 ( chia là nhân nghịch đảo)
= 1/5 x 5/2
=1/2 hay 0,5