BÀI KHÓ THẾ ANH LỚP 9 EM LOPWS4 HIHI

1. a. \(\sqrt{x}\)\(\ge\)0  => \(\sqrt{x}+5\ge5\)

b.\(\sqrt{x}\ge0\Rightarrow3\sqrt{x}\ge0\Rightarrow3\sqrt{x}-2\ge-2\)

cos36^o =  (1+√5)/4

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Bài 2 : 

a, \(\sqrt{0,09}=\sqrt{\frac{9}{100}}=\frac{3}{10}\)

b, \(\sqrt{-16}\)vô lí vì \(\sqrt{a}\)xảy ra khi a >= 0 mà -16 < 0 

c, \(\sqrt{0,25}.\sqrt{0,16}=\sqrt{\frac{25}{100}}.\sqrt{\frac{16}{100}}=\frac{5}{10}.\frac{4}{10}=\frac{20}{100}=\frac{1}{5}\)

e, \(\sqrt{\frac{4}{25}}=\frac{2}{5}\); f, \(\frac{6\sqrt{16}}{5\sqrt{0,04}}=\frac{24}{5\sqrt{\frac{4}{100}}}=\frac{24}{\frac{10}{10}}=24\)

g, \(\sqrt{0,36}-\sqrt{0,49}=\sqrt{\frac{36}{100}}-\sqrt{\frac{49}{100}}=\frac{6}{10}-\frac{7}{10}=-\frac{1}{10}\)

a, \(\sqrt{x-6}=13\)ĐK : x >= 6

\(\Leftrightarrow x-6=169\Leftrightarrow x=175\)

b, \(\sqrt{x^2-2x+4}=x-1\Leftrightarrow x^2-2x+4=x^2-2x+1\)

\(\Leftrightarrow4=1\)( vô lí ), vậy pt vô nghiệm 

c, \(\sqrt{x^2-8x+16}=9x-1\Leftrightarrow\left|x-4\right|=9x-1\)

ĐK : x >= 1/9

TH1 : \(x-4=9x-1\Leftrightarrow-8x=3\Leftrightarrow x=-\frac{3}{8}\)( ktm ) 

TH2 : \(x-4=1-9x\Leftrightarrow10x=5\Leftrightarrow x=\frac{1}{2}\)( tm )

c, \(\sqrt{x^2-x-4}=\sqrt{x-1}\Leftrightarrow x^2-x-4=x-1\)

\(\Leftrightarrow x^2-2x-3=0\Leftrightarrow x=3;x=-1\)

e, \(\sqrt{x^2-4x+4}=\sqrt{4x^2-12x+9}\)

\(\Leftrightarrow\left|x-2\right|=\left|2x-3\right|\)

TH1 : \(x-2=2x-3\Leftrightarrow x=1\)

TH2 : \(x-2=3-2x\Leftrightarrow3x=5\Leftrightarrow x=\frac{5}{3}\)

g, \(\sqrt{x+2\sqrt{x-1}}=2\)ĐK : x > = 1 

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

\(\Leftrightarrow\sqrt{\left(\sqrt{x-1}+1\right)^2}=2\Leftrightarrow\left|\sqrt{x-1}+1\right|=2\)

TH1 : \(\sqrt{x-1}+1=2\Leftrightarrow\sqrt{x-1}=1\Leftrightarrow x-1=1\Leftrightarrow x=2\)

TH2 : \(\sqrt{x-1}+1=-2\)( vô lí )