rút gọn
\(N=\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\frac{2x+\sqrt{x}}{\sqrt{x}}+\frac{2\left(x-1\right)}{\sqrt{x}-1}\)\(\left(x>0,x\ne1\right)\)
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\(f,x^2-2\sqrt{5}x+5=0\)
\(\left(x-\sqrt{5}\right)^2=0\)
\(x-\sqrt{5}=0\)
\(x=\sqrt{5}\)
\(g,\sqrt{x^2-4x+4}-\sqrt{x^2+2x+1}=-3\)
\(\sqrt{\left(x-2\right)^2}-\sqrt{\left(x+1\right)^2}=-3\)
\(\left|x-2\right|-\left|x+1\right|=-3\)
lập bảng xét dấu:
\(TH1:x\le-1\)
\(2-x+x+1=-3\)
\(3=-3\left(KTM\right)\)
\(TH2:-1< x\le2\)
\(2-x-x-1=-3\)
\(2x=4\)
\(x=2\left(TM\right)\)
\(TH3:x>2\)
\(x-2-x-1=-3\)
\(0x=0\)
pt vô số n0 kết hợp với đkxđ
\(x>2\)
Trả lời:
f) \(x^2-2\sqrt{5}x+5=0\)
\(\Leftrightarrow x^2-2.x.\sqrt{5}+\left(\sqrt{5}\right)^2=0\)
\(\Leftrightarrow\left(x-\sqrt{5}\right)^2=0\)
\(\Leftrightarrow x-\sqrt{5}=0\)
\(\Leftrightarrow x=\sqrt{5}\)
\(=\sqrt{7}-\sqrt{4-2.2\sqrt{7}+7}\)
\(=\sqrt{7}-\sqrt{\left(2-\sqrt{7}\right)^2}\)
\(=\sqrt{7}-\sqrt{7}+2=2\)
\(\sqrt{7}-\sqrt{11-4\sqrt{7}}\)
\(=\sqrt{7}-\sqrt{\sqrt{7}^2-2\cdot\sqrt{7}\cdot2+2^2}\)
\(=\sqrt{7}-\sqrt{\left(\sqrt{7}-2\right)^2}\)
\(=\sqrt{7}-\left|\sqrt{7}-2\right|\)
\(=\sqrt{7}-\sqrt{7}+2=2\)
\(5\sqrt{34}+\left|6-\sqrt{34}\right|\)
\(6>\sqrt{34}\)
\(5\sqrt{34}+6-\sqrt{34}\)
\(4\sqrt{34}+6\)
a) Ta có:
\(\sqrt{\frac{289}{225}}=\sqrt{\frac{\sqrt{289}}{\sqrt{225}}}=\sqrt{\frac{17^2}{15^2}}=\frac{17}{15}\)
b) Ta có:
\(\sqrt{2\frac{14}{25}}=\sqrt{\frac{64}{25}}=\sqrt{\frac{\sqrt{64}}{\sqrt{25}}}=\sqrt{\frac{8^2}{5^2}}=\frac{8}{5}\)
c) Ta có:
\(\sqrt{\frac{0,25}{9}}=\sqrt{\frac{\sqrt{0,25}}{\sqrt{9}}}=\sqrt{\frac{0,5^2}{3^2}}=\frac{0,5}{3}=\frac{1}{6}\)
d) Ta có:
\(\sqrt{\frac{8,1}{1,6}}=\sqrt{\frac{81.0,1}{16.0,1}}=\sqrt{\frac{81}{16}}=\sqrt{\frac{\sqrt{81}}{\sqrt{16}}}=\sqrt{\frac{9^2}{4^2}}=\frac{9}{4}\)
a)Ta có: \(\sqrt{\frac{289}{225}}=\frac{\sqrt{289}}{\sqrt{225}}=\frac{17}{15}\)
b) Ta có: \(\sqrt{2\frac{14}{25}}=\sqrt{\frac{64}{25}}=\frac{\sqrt{64}}{\sqrt{25}}=\frac{8}{5}\)
c) Ta có: \(\sqrt{\frac{0,25}{9}}=\frac{\sqrt{0,25}}{\sqrt{9}}=\frac{0,5}{3}=\frac{1}{6}\)
d)Ta có : \(\sqrt{\frac{8,1}{1,6}}=\frac{\sqrt{8,1}}{\sqrt{1,6}}=\frac{\sqrt{8,1}.100}{\sqrt{1,6}.100}=\frac{\sqrt{81}}{\sqrt{16}}=\frac{9}{4}\)
\(N=\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\frac{2x+\sqrt{x}}{\sqrt{x}}+\frac{2\left(x-1\right)}{\sqrt{x}-1}\)
\(=\frac{\sqrt{x}\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{x+\sqrt{x}+1}-\frac{\sqrt{x}\left(2\sqrt{x}+1\right)}{\sqrt{x}}+\frac{2\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}-1}\)
\(=\sqrt{x}\left(\sqrt{x}-1\right)-\left(2\sqrt{x}+1\right)+2\left(\sqrt{x}+1\right)\)
\(=x-\sqrt{x}-2\sqrt{x}-1+2\sqrt{x}+2\)
\(=x-\sqrt{x}+1\)