số hs khá là: \(\dfrac{3}{4}\times\dfrac{1}{6}=\dfrac{1}{8}\left(hs\right)\)

a: số hs lớp 6A là : \(\dfrac{3}{4}+\dfrac{1}{8}+5=\dfrac{18}{24}+\dfrac{3}{24}+5=5\dfrac{21}{24}=5\dfrac{7}{8}=\dfrac{47}{8}\left(hs\right)\)

b: tỉ số là : \(\dfrac{3}{4}\times100:\dfrac{1}{8}=\dfrac{300}{4}:\dfrac{1}{8}=\dfrac{300\times8}{4\times1}=600\%\)

Gọi học sinh lớp 6a là x hs

Số học sinh giỏi là : \(\dfrac{3}{4}x\)(hs)

Số học sinh khác là : \(\dfrac{1}{6}.\dfrac{3}{4}x=\dfrac{1}{8}x\) (hs)

Theo bài ra có :

\(x-\dfrac{3}{4}x-\dfrac{1}{8}x=5\)

\(x\left(1-\dfrac{3}{4}-\dfrac{1}{8}\right)=5\)

\(\dfrac{1}{8}x=5\)

\(x=40\)

Vậy số hcj sinh lớp 6a là 40 hs

Số học sinh giỏi là : \(\dfrac{3}{4}.40=30\) (hs)

Số học sinh khá là :\(\dfrac{1}{6}.30=5\) (hs)

ĐS ...

\(b,\Leftrightarrow\left\{{}\begin{matrix}m+1=3\\m-3\ne-3\end{matrix}\right.\Leftrightarrow m=2\\ c,\text{PT giao Ox tại hoành độ 3: }\\ x=-3;y=0\Leftrightarrow\left(m+1\right)\left(-3\right)+m-3=0\\ \Leftrightarrow-2m-6=0\Leftrightarrow m=-3\)

\(\dfrac{x+4}{3}=\dfrac{x-11}{-6}\)

\(\dfrac{2x+8}{6}=\dfrac{-x+11}{6}\)

\(\Leftrightarrow2x+8=-x+11\)

\(\Leftrightarrow3x=3\)

\(\Leftrightarrow x=1\)

Nhân chéo ta được\(-6(x+4)=3(x-11)=>-6x-24=3x-33=>6x-3x-24+33=0=>3x+9=0=>3x=-9=>x=-3\)

Chắc đề đúng là \(\dfrac{1}{4+1^4}+\dfrac{3}{4+3^4}+...\)

- Với \(n=1\) đẳng thức đúng

- Giả sử đẳng thức cũng đúng với \(n=k>1\) hay:

\(\dfrac{1}{4+1^4}+\dfrac{3}{4+3^4}+...+\dfrac{2k-1}{4+\left(2k-1\right)^4}=\dfrac{k^2}{4k^2+1}\)

- Ta cần chứng minh nó cũng đúng với \(n=k+1\) hay:

\(\dfrac{1}{4+1^4}+\dfrac{3}{4+3^4}+...+\dfrac{2k-1}{4+\left(2k-1\right)^4}+\dfrac{2k+1}{4+\left(2k+1\right)^4}=\dfrac{\left(k+1\right)^2}{4\left(k+1\right)^2+1}\)

Thật vậy, ta có:

\(\dfrac{1}{4+1^4}+\dfrac{3}{4+3^4}+...+\dfrac{2k-1}{4+\left(2k-1\right)^4}+\dfrac{2k+1}{4+\left(2k+1\right)^4}=\dfrac{k^2}{4k^2+1}+\dfrac{2k+1}{4+\left(2k+1\right)^4}\)

\(=\dfrac{k^2}{4k^2+1}+\dfrac{2k+1}{\left(2k+1\right)^4+4\left(2k+1\right)^2+4-4\left(2k+1\right)^2}=\dfrac{k^2}{4k^2+1}+\dfrac{2k+1}{\left(4k^2+4k+3\right)^2-\left(4k+2\right)^2}\)

\(=\dfrac{k^2}{4k^2+1}+\dfrac{2k+1}{\left(4k^2+1\right)\left(4k^2+8k+5\right)}=\dfrac{k^2\left(4k^2+8k+5\right)+2k+1}{\left(4k^2+1\right)\left(4k^2+8k+5\right)}\)

\(=\dfrac{\left(k+1\right)^2\left(4k^2+1\right)}{\left(4k^2+1\right)\left(4k^2+8k+5\right)}=\dfrac{\left(k+1\right)^2}{4k^2+8k+5}=\dfrac{\left(k+1\right)^2}{4\left(k+1\right)^2+1}\) (đpcm)

a, thay x=25 vào A ta có:

\(A=\dfrac{\sqrt{x}}{\sqrt{x}-1}=\dfrac{\sqrt{25}}{\sqrt{25}-1}=\dfrac{5}{5-1}=\dfrac{5}{4}\)

b, \(P=\dfrac{\sqrt{x}}{\sqrt{x}-1}\left(\dfrac{3x+3}{x\sqrt{x}-1}-\dfrac{2}{\sqrt{x}-1}\right)\)

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

\(\Rightarrow P=\dfrac{\sqrt{x}}{\sqrt{x}-1}\left(\dfrac{3x+3}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}-\dfrac{2x+2\sqrt{x}+2}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\right)\)

\(\Rightarrow P=\dfrac{\sqrt{x}}{\sqrt{x}-1}.\dfrac{3x+3-2x-2\sqrt{x}-2}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)

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

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

\(\Rightarrow P=\dfrac{\sqrt{x}}{x+\sqrt{x}+1}\)

cái này thì triệt tiêu ra đó bn

là bằng 2020/6069

A = 1/3.5.7 + 1/5.7.9+ ... + 1/2019.2021.2023

2A = 2/3.5.7 + 2/5.7.9+ ... + 2/2019.2021.2023

2A = 1/3-1/5+1/7+1/5-1/7+1/9+....+1/2019-1/2021+1/2023

2A = 1/3 - 1/2023

2A = 2023/6069 - 3/6069

2A = 2023-3/6069

2A = 2020/6069

 A = 1010/6069

Vậy A = 1010/6069

\(=2\sqrt{3}-10\sqrt{3}-\sqrt{3}+\dfrac{5\sqrt{3}}{2}=\dfrac{5\sqrt{3}}{2}-9\sqrt{3}=\dfrac{5\sqrt{3}-18\sqrt{3}}{2}=\dfrac{-13\sqrt{3}}{2}\)

\(=\dfrac{1}{2}.4\sqrt{3}-2.5\sqrt{3}-\sqrt{3}+5.\dfrac{\sqrt{3}}{2}\)

\(=2\sqrt{3}-10\sqrt{3}-\sqrt{3}+\dfrac{5\sqrt{3}}{2}\)

\(=-9\sqrt{3}+\dfrac{5\sqrt{3}}{2}=\dfrac{-18\sqrt{3}+5\sqrt{3}}{2}=-\dfrac{13\sqrt{3}}{2}\)

Giải hpt:

Đặt: \(\left[{}\begin{matrix}\sqrt{x-1}=a\\y+1=b\end{matrix}\right.\)

Ta có: \(\left\{{}\begin{matrix}3a-2b=-1\\5a-9b=-13\end{matrix}\right.< =>\left\{{}\begin{matrix}15a-10b=-5\\15a-27b=-39\end{matrix}\right.< =>\left\{{}\begin{matrix}b=2\\15a-27\cdot2=-39\end{matrix}\right.< =>\left\{{}\begin{matrix}b=2\\a=1\end{matrix}\right.\)

Thay: \(\left[{}\begin{matrix}\sqrt{x-1}=1\\y+1=2\end{matrix}\right.< =>\left[{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)