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M= \(\sqrt{2}+1-\) \(\sqrt{\left(\sqrt{2}-1\right)^2}=\sqrt{2}+1-\sqrt{2}+1=2\)
N=\(\sqrt{1+2\sqrt{\left(\sqrt{2}+1\right)^2}}=\sqrt{1+2\left(\sqrt{2}+1\right)}=\) \(\sqrt{1+2\sqrt{2}+2}=\sqrt{\left(\sqrt{2}+1\right)^2}=\sqrt{2}+1\)
P= \(\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}-1}+\frac{2\sqrt{x}.\sqrt{x}}{\sqrt{x}}\) (dk \(x>0\))
=\(\sqrt{x}+1+2\sqrt{x}=3\sqrt{x}+1\)
Q= \(\sqrt{\left(\sqrt{x}+1\right)^2}+\sqrt{\left(\sqrt{x}-1\right)^2}\) (dk \(x\ge0\) )
=\(\left|\sqrt{x}+1\right|+\left|\sqrt{x}-1\right|\)
th1 \(\sqrt{x}\ge1\Leftrightarrow x\ge1\) Q=\(\sqrt{x}+1+\sqrt{x}-1=2\sqrt{x}\)
th2 \(0\le x< 1\) Q=\(\sqrt{x}+1+1-\sqrt{x}=2\)
a) \(M=\sqrt{2}+1-\sqrt{1,5.2-2.\sqrt{2}}\)
\(=\sqrt{2}+1-\sqrt{2.\left(1,5-\sqrt{2}\right)}\)\(=\sqrt{2}+1-\sqrt{2}.\sqrt{1,5-\sqrt{2}}\)
\(=\sqrt{2}.\left(1+1,5-\sqrt{2}\right)+1=\sqrt{2}.\left(2,5-\sqrt{2}\right)+1\)
\(=\sqrt{2}.2,5-2+1=\sqrt{2}.2,5-1\)
P/s: Theo em thì em nghĩ là đúng '-' Khoảng 90% :)
\(M=\left(\frac{x+2}{x\sqrt{x-1}}+\frac{\sqrt{x}}{x+\sqrt{x+1}}-\frac{1}{\sqrt{x}-1}\right):\frac{\sqrt{x}-1}{7}\)
\(=\left[\frac{x+2}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}+\frac{\sqrt{x}}{x+\sqrt{x}+1}-\frac{1}{\sqrt{x}-1}\right]:\frac{\sqrt{x}-1}{7}\)
\(=\left[\frac{x+2+\sqrt{x}\left(\sqrt{x}-1\right)-\left(x+\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\right]:\frac{\sqrt{x}-1}{7}\)
\(=\left[\frac{x+2+x-\sqrt{x}-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\right]:\frac{\sqrt{x}-1}{7}\)
\(=\frac{x+1-2\sqrt{x}}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}.\frac{7}{\sqrt{x}-1}\)
\(=\frac{\left(\sqrt{x}-1\right)^2.7}{\left(\sqrt{x}-1\right)^2\left(x+\sqrt{x}+1\right)}\)
\(=\frac{7}{x+\sqrt{x}+1}\)
Giúp với mình gấp quá
\(=\frac{2\sqrt{x}}{\sqrt{x}-1}-\frac{x+1}{x-1}\)
\(=\frac{2\sqrt{x}\left(x-1\right)-\left(x+1\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(x-1\right)}\)
\(=\frac{2x\sqrt{x}-2\sqrt{x}-x\sqrt{x}+x-\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(x-1\right)}\)
\(=\frac{x\sqrt{x}-\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(x-1\right)}\)
\(=\frac{x\sqrt{x}-\sqrt{x}+1}{x\sqrt{x}-\sqrt{x}-x+1}=1-\frac{x}{\left(\sqrt{x}-1\right)\left(x-1\right)}\)