\(A=3\sqrt{3}-8\sqrt{3}+15\sqrt{3}=10\sqrt{3}\)

\(B=\left|\sqrt{5}-2\right|-\left|\sqrt{5}-3\right|=\sqrt{5}-2-\left(\sqrt{5}-3\right)=\sqrt{5}-2-\sqrt{5}+3=1\)

\(C=\left|2\sqrt{3}+1\right|+\left|2\sqrt{3}-5\right|=2\sqrt{3}+1+5-2\sqrt{3}=6\)

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

\(E=\frac{4\left(\sqrt{5}+2\right)}{5-4}-\frac{32\left(\sqrt{5}-1\right)}{5-1}=4\sqrt{5}+8-\frac{32\sqrt{5}-32}{4}=4\sqrt{5}+8-8\sqrt{5}+8=16-4\sqrt{5}\)

\(M=\frac{10\left(3\sqrt{2}+4\right)}{18-16}+\frac{28\left(3\sqrt{2}-2\right)}{18-4}=\frac{30\sqrt{2}+40}{2}+\frac{84\sqrt{2}-56}{14}=15\sqrt{2}+20+6\sqrt{2}-4=16+21\sqrt{2}\)

hỏi văn hay hỏi toán z

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Bài 2. 

\(x^2-2mx+4=0\)(2) 

a) Với \(m=3\)(2) trở thành: 

\(x^2-6x+4=0\)

\(\Leftrightarrow x^2-6x+9=5\)

\(\Leftrightarrow\left(x-3\right)^2=5\)

\(\Leftrightarrow x=\pm\sqrt{5}+3\)

b) Để (1) có hai nghiệm phân biệt \(x_1\), \(x_2\)thì \(\Delta'>0\).

\(\Delta'=m^2-4>0\Leftrightarrow\orbr{\begin{cases}m>2\\m< -2\end{cases}}\)

Theo Viete:

\(\hept{\begin{cases}x_1+x_2=2m\\x_1x_2=4\end{cases}}\)

\(\left(x_1+1\right)^2+\left(x_2+1\right)^2=x_1^2+x_2^2+2\left(x_1+x_2\right)+2\)

\(=\left(x_1+x_2\right)^2-2x_1x_2+2\left(x_1+x_2\right)+2\)

\(=4m^2-8+4m+2=2\)

\(\Leftrightarrow m^2+m-2=0\)

\(\Leftrightarrow\orbr{\begin{cases}m=1\left(l\right)\\m=-2\left(l\right)\end{cases}}\)

Bài 1. 

a) Với \(m=-3\): (1) trở thành:

\(x^2+6x-7=0\)

\(\Leftrightarrow\left(x+7\right)\left(x-1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=-7\\x=1\end{cases}}\)

b) Để (1) có hai nghiệm phân biệt \(x_1\), \(x_2\)thì \(\Delta'>0\).

\(\Delta'=m^2-\left(2m-1\right)=m^2-2m+1=\left(m-1\right)^2\)

\(\left(m-1\right)^2>0\Leftrightarrow m\ne1\).

Theo Viete ta có: 

\(\hept{\begin{cases}x_1+x_2=2m\\x_1x_2=2m-1\end{cases}}\)

\(2\left(x_1^2+x_2^2\right)-5x_1x_2=2\left[\left(x_1+x_2\right)^2-2x_1x_2\right]-5x_1x_2\)

\(=2\left[\left(2m\right)^2-2\left(2m-1\right)\right]-5\left(2m-1\right)=8m^2-18m+9=27\)

\(\Leftrightarrow8m^2-18m-18=0\)

\(\Leftrightarrow\orbr{\begin{cases}m=3\\m=-\frac{3}{4}\end{cases}}\)(thỏa mãn)

\(x-\sqrt{x}=m\Leftrightarrow x-\sqrt{x}-m=0\)

\(\Delta=1-4\left(-m\right)=1+4m\)

Để phương trình trên có nghiệm khi \(\Delta\ge0\)

\(1+4m\ge0\Leftrightarrow m\ge-\frac{1}{4}\)

sửa đề : 

\(N=\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right):\left(\frac{\sqrt{x}-1}{\sqrt{x}}+\frac{1-\sqrt{x}}{x+\sqrt{x}}\right)\)đk : x >= 0 

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

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

n = (\(\sqrt{yyx}\)-r554-56