a)\(1+\sqrt{3}>1+\sqrt{1}=1+1=2\)

Vậy \(1+\sqrt{3}>2\)

c) \(\sqrt{3}-1< \sqrt{4}-1=2-1=1\)

Vậy \(\sqrt{3}-1< 1\)

e) \(\sqrt{2}+\sqrt{5}< \sqrt{16}+\sqrt{16}=4+4=8\)

Vậy \(\sqrt{2}+\sqrt{5}< 8\)

min của \(A=a^2+b^2+c^2-2\sqrt{3abc}\) chứ nhỉ

à nhầm

a. Ta có: \(A=\sqrt{x-2\sqrt{1}}+\sqrt{x-1}=\sqrt{x-2}+\sqrt{x-1}\).

b. Với x = 5 thì \(A=\sqrt{5-2}+\sqrt{5-1}=\sqrt{3}+\sqrt{4}=2+\sqrt{3}\).

= 2,015625478

~ Good Luck ~

Sai thì bỏ qua mk nhé!!

#)Trả lời :

\(=\sqrt{3\left(4-\sqrt{7}\right)}\)

a) \(\sqrt{x^2-x-2}-\sqrt{x-2}=0\)

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

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

\(\Leftrightarrow x^2-x-2=x-2\)

\(\Leftrightarrow\orbr{\begin{cases}x=2\left(tm\right)\\x=0\left(\text{loại}\right)\end{cases}}\)

=> x = 2

b) \(\sqrt{x^2+x-2}=\sqrt{x^2-2}\)

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

\(\Leftrightarrow x^2+x-2=x^2-2\)

\(\Leftrightarrow x=0\)

=> k có x thỏa mãn

b) \(\sqrt{x^2-9}-3\sqrt{x-3}=0\)

\(\Leftrightarrow\sqrt{x^2-3^2}-3\sqrt{x-3}=0\)

\(\Leftrightarrow\sqrt{\left(x+3\right)\left(x-3\right)}-3\sqrt{x-3}=0\)

\(\Leftrightarrow\sqrt{\left(x+3\right)}\sqrt{x-3}-3\sqrt{x-3}=0\)

\(\Leftrightarrow\sqrt{x-3}\left(\sqrt{x+3}+3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}\sqrt{x-3}=0\\\sqrt{x+3}+3=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3\\x\in\left\{\varnothing\right\}\end{cases}}\)

Vậy nghiệm duy nhất của pt là 3.

Quên. Nghiệm thứ hai \(\sqrt{x+3}-3=0\)

\(\Leftrightarrow\sqrt{x+3}=3\)

\(\Leftrightarrow x+3=9\)

\(\Leftrightarrow x=6\)

Vậy pt có 2 nghiệm là 3 và 6

a/ \(đkxđ\) : \(x\ne0;x\ne1\)

b/ 

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

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

\(=\frac{\left(x-2\sqrt{x}+1\right).\sqrt{x}-\left(x+\sqrt{x}\right)\left(\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}\)

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

\(=\frac{2\sqrt{x}-2x}{\sqrt{x}\left(\sqrt{x}-1\right)}\)

\(=\frac{2\sqrt{x}\left(1-\sqrt{x}\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}\)

\(=-2\)

chúc bn học tốt

\(a,\sqrt{33+20\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)

\(=\sqrt{8+2.2\sqrt{2}.5+25}-\sqrt{2-2.\sqrt{2}.3+9}\)

\(=\sqrt{\left[2\sqrt{2}+5\right]^2}-\sqrt{\left[\sqrt{2}-3\right]^2}\)

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

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

chúc bn học tốt

a) \(\sqrt{\left(2\sqrt{2}+5\right)^2}\) \(-\) \(\sqrt{\left(3-\sqrt{2}\right)^2}\)= \(|2\sqrt{2}+5|\)\(-\)\(|3-\sqrt{2}|\)

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

b)\(\sqrt{\left(7-3\sqrt{5}\right)^2}-\sqrt{\left(7+3\sqrt{5}\right)^2}=7-3\sqrt{5}-7-3\sqrt{5}=-6\sqrt{5}\)

a, \(\sqrt{3-\sqrt{5}}+\sqrt{7-3\sqrt{5}}\)\(=\sqrt{\frac{1}{2}.\left(6-2\sqrt{5}\right)}\)\(+\sqrt{\frac{1}{2}.\left(14-2.3\sqrt{5}\right)}\)

\(=\sqrt{\frac{1}{2}.\left(\sqrt{5}-1\right)^2}\)\(+\sqrt{\frac{1}{2}.\left(3-\sqrt{5}\right)^2}\)\(=\frac{\sqrt{2}}{2}.\left(\sqrt{5}-1\right)+\frac{\sqrt{2}}{2}.\left(3-\sqrt{5}\right)\)

\(=\frac{\sqrt{2}}{2}.2=\sqrt{2}\)

Câu b đề đúng ko bn

ta có \(n_{CuO}=\frac{8}{80}=0,1\left(mol\right)\)

pứ : \(CuO+H_2SO_4\rightarrow CuSO_4+H_2O\left(1\right)\)

      \(0,1\rightarrow0,1\rightarrow0,1\rightarrow0,1\left(mol\right)\)

theo pứ \(\left(1\right)\) có \(n_{H_2SO_4}=0,1\left(mol\right)\)

\(\rightarrow\) \(C\%_{H_2SO_4}=\frac{m_{H_2SO_4}}{m_{dungdịch}}=\frac{0,1.98}{100}.100=9,8\%\)

theo pứ \(\left(1\right)\) có : \(n_{CuSO_4}=0,1\left(mol\right)\)

\(\rightarrow\)\(C\%_{CuSO_4}=\frac{^mCuSO_4}{m_{dungdichsaupu}}=\frac{0,1.160}{8+100}.100\%\approx14,81\%\)

chúc bn học tốt