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8: DKXĐ: x-1>=0 và 2-2x>=0
=>x>=1 và x<=1
=>x=1
9: ĐKXĐ: x^2-1>=0 và 4-4x^2>=0
=>x^2>=1 và x^2<=1
=>x^2=1
=>x=1 hoặc x=-1
10: ĐKXĐ: x-1>=0 và 3-x>=0
=>1<=x<=3
`1a)A=(5sqrt5+2sqrt{45}+sqrt5).sqrt5`
`=(5sqrt{5}+2sqrt{9.5}+sqrt5).sqrt5`
`=(5sqrt5+6sqrt5+sqrt5).sqrt5`
`=12sqrt5*sqrt5=60`
`b)B=2sqrt2+1/(2sqrt2)-4sqrt{50}`
`=2sqrt2+1/(2sqrt2)-4.sqrt{25.2}`
`=2sqrt2+1/(2sqrt2)-20sqrt2`
`=(8+1-80)/(2sqrt2)`
`=(-71)/(2sqrt2)`
`=(-71sqrt2)/4`
`c)=1/(1-sqrt2)+1/(1+sqrt2)`
`=(sqrt2+1)/(1-2)+(sqrt2-1)/(2-1)`
`=-sqrt2-1+sqrt2-1=-2`
`2)sqrt{(8-4x)^2}=2`
`<=>|8-4x|=2`
`<=>|4-2x|=1`
`<=>` \(\left[ \begin{array}{l}4-2x=1\\4-2x=-1\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}2x=3\\2x=5\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x=\dfrac32\\x=\dfrac52\end{array} \right.\)
Vậy `S={3/2,5/2}`
\(A=\left(5\sqrt{5}+6\sqrt{5}+\sqrt{5}\right).\sqrt{5}=12\sqrt{5}.\sqrt{5}=12.5=60\)
\(B=2\sqrt{2}+\dfrac{1}{2}\sqrt{2}-10\sqrt{2}=-7,5.\sqrt{2}\)
\(C=\dfrac{1}{1-\sqrt{2}}+\dfrac{1}{1+\sqrt{2}}=\dfrac{1+\sqrt{2}}{-1}+\dfrac{1-\sqrt{2}}{-1}=-1-\sqrt{2}-1+\sqrt{2}=-2\)
Bài 2:
\(\sqrt{\left(8-4x\right)^2}=2\)
*TH1: x < 2
\(\sqrt{\left(8-4x\right)^2}=2\)
\(\Leftrightarrow8-4x=2\Leftrightarrow4x=6\Leftrightarrow x=\dfrac{6}{4}=\dfrac{3}{2}\)
*TH2: x ≥ 2
\(\sqrt{\left(8-4x\right)^2}=2\)
\(\Leftrightarrow4x-8=2\Leftrightarrow4x=10\Leftrightarrow x=\dfrac{10}{4}=\dfrac{5}{2}\)
Câu 1:
\(a^2+2ab+b^2-ac-bc\)
\(=\left(a+b\right)^2-c\left(a+b\right)\)
\(=\left(a+b\right)\left(a+b-c\right)\)
Câu 2:
\(5x^2-5y^2-10x+10y\)
\(=5\left(x-y\right)\left(x+y\right)-10\left(x-y\right)\)
\(=\left(x-y\right)\left(5x+5y-10\right)\)
\(=5\left(x-y\right)\left(x+y-2\right)\)
Câu 3:
\(3x^2-6xy+3y^2-12z^2\)
\(=3\left[\left(x-y\right)^2-4z^2\right]\)
\(=3\left(x-y-2z\right)\left(x-y+2z\right)\)
Câu 4:
\(x^4+x^3+x^2-1\)
\(=x^3\left(x+1\right)+\left(x-1\right)\left(x+1\right)\)
\(=\left(x+1\right)\left(x^3+x-1\right)\)
Câu 5:
\(x^3-3x^2+3x-1-y^3\)
\(=\left(x-1\right)^3-y^3\)
\(=\left(x-1-y\right)\left[\left(x-1\right)^2+\left(x-1\right)y+y^2\right]\)
\(=\left(x-y-1\right)\left(x^2-2x+1+xy-y+y^2\right)\)
Câu 6:
\(x^4-x^2+2x-1\)
\(=x^4-\left(x-1\right)^2\)
\(=\left(x^2-x+1\right)\left(x^2+x-1\right)\)
Câu 7:
\(\left(x+y\right)^3-x^3-y^3\)
\(=\left(x+y\right)^3-\left[\left(x+y\right)^3-3xy\left(x+y\right)\right]\)
\(=3xy\left(x+y\right)\)
D
\(tanE=\dfrac{DF}{DE}=\dfrac{\sqrt{5^2-1}}{1}=2\sqrt{6}\)
D