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Đề đâu??????

\(\frac{\left(\sqrt{2}+\sqrt{3}+\sqrt{6}\right)\left(2\sqrt{6}+1\right)}{23}\)

cảm ơn bạn alibaba nguyễn

Đặt \(A=\frac{a}{\sqrt{a^2-b^2}}-\left(1+\frac{a}{\sqrt{a^2-b^2}}\right):\frac{b}{a-\sqrt{a^2-b^2}}\)

\(A=\frac{a}{\sqrt{a^2-b^2}}-\frac{\left(a+\sqrt{a^2-b^2}\right)\left(a-\sqrt{a^2-b^2}\right)}{b\sqrt{a^2-b^2}}\)

\(A=\frac{a}{\sqrt{a^2-b^2}}-\frac{a^2-a^2+b^2}{b\sqrt{a^2-b^2}}\)

\(A=\frac{a}{\sqrt{a^2-b^2}}-\frac{b}{\sqrt{a^2-b^2}}\)

\(A=\frac{a-b}{\sqrt{a-b}.\sqrt{a+b}}\)

\(A=\frac{\sqrt{a-b}}{\sqrt{a+b}}\)

Với \(a=3b\) ta có : \(A=\frac{\sqrt{a-b}}{\sqrt{a+b}}=\frac{\sqrt{3b-b}}{\sqrt{3b+b}}=\frac{\sqrt{2b}}{\sqrt{4b}}=\frac{\sqrt{2}}{2}\)

Chúc bạn học tốt ~ 

mn làm giúp mk vs

\(\frac{a}{\sqrt{a^2-b^2}}-\left(1+\frac{a}{\sqrt{a^2-b^2}}\right):\frac{b}{a-\sqrt{a^2-b^2}}\)

\(=\frac{a}{\sqrt{a^2-b^2}}-\frac{a+\sqrt{a^2-b^2}}{\sqrt{a^2-b^2}}.\frac{a-\sqrt{a^2-b^2}}{b}\)

\(=\frac{a}{\sqrt{a^2-b^2}}-\frac{a^2-a^2+b^2}{\sqrt{a^2-b^2}b}\)

\(=\frac{ab-a^2+a^2-b^2}{\sqrt{a^2-b^2}b}\)

\(=\frac{b\left(a-b\right)}{\sqrt{\left(a-b\right)\left(a+b\right)}b}\)

\(=\frac{\sqrt{a-b}}{\sqrt{a+b}}\)

b, Thay a = 3b

\(=\sqrt{\frac{3b-b}{3b+b}}=\sqrt{\frac{2}{4}}=\sqrt{\frac{1}{2}}\)

Ta có: \(\sqrt{18}-\frac{1}{3}\sqrt{72}-\sqrt{8}+\frac{2-3\sqrt{2}}{3-\sqrt{2}}\)

\(=3\sqrt{2}-\frac{6\sqrt{2}}{3}-2\sqrt{2}+\frac{\left(3+\sqrt{2}\right)\left(2-3\sqrt{2}\right)}{9-2}\)

\(=3\sqrt{2}-2\sqrt{2}-2\sqrt{2}-\sqrt{2}\)

\(=-2\sqrt{2}\)

xin lỗi em mới lớp 8 ko trả lời dc

a: ĐKXĐ: \(\left\{{}\begin{matrix}a>=0\\a< >1\end{matrix}\right.\)

\(A=\dfrac{1}{2\left(\sqrt{a}+1\right)}-\dfrac{1}{2\left(\sqrt{a}-1\right)}+\dfrac{a^2+1}{a^2-1}\)

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

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

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

b: Để A-1/3<0 thì \(\dfrac{a}{a+1}-\dfrac{1}{3}< 0\)

=>3a-a-1<0

=>2a-1<0

hay 0<a<1/2

\(x=\frac{1}{2}\sqrt{\sqrt{2}+\frac{1}{8}}-\frac{1}{8}\sqrt{2}\)

\(\Leftrightarrow x+\frac{\sqrt{2}}{8}=\frac{1}{2}\sqrt{\sqrt{2}+\frac{1}{8}}\)

\(\Leftrightarrow\left(x+\frac{\sqrt{2}}{8}\right)^2=\frac{1}{4}\left(\sqrt{2}+\frac{1}{8}\right)\)

\(\Leftrightarrow x^2+\frac{x\sqrt{2}}{4}+\frac{1}{32}=\frac{\sqrt{2}}{4}+\frac{1}{32}\)

\(\Leftrightarrow x^2+\frac{x\sqrt{2}}{4}-\frac{\sqrt{2}}{4}=0\)

\(\Leftrightarrow4x^2+x\sqrt{2}-\sqrt{2}=0\)(1)

\(\Leftrightarrow x\sqrt{2}=\sqrt{2}-4x^2\)

\(\Leftrightarrow x=1-2x^2\sqrt{2}\)

Thay vào M ta sẽ được

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

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

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

Từ \(\left(1\right)\Rightarrow\sqrt{2}-x\sqrt{2}=4x^2\ge0\)

           \(\Leftrightarrow\sqrt{2}\left(1-x\right)\ge0\)

           \(\Leftrightarrow x\le1\)

           \(\Leftrightarrow x^2\le1< \sqrt{2}\)

           \(\Rightarrow\left|x^2-\sqrt{2}\right|=\sqrt{2}-x^2\)

Khi đó \(M=x^2+\left|x^2-\sqrt{2}\right|=x^2-\sqrt{2}+x^2=\sqrt{2}\)

|N|

ta có ĐK là x>=0

ta có \(4\sqrt{x}\ge0;x+2\sqrt{x}+1>0\Rightarrow\) \(\frac{4\sqrt{x}}{x+2\sqrt{x}+1}\ge0\)

dấu = xảy ra <=> x= 0,