Question

[Ly Ly]

Câu 1: Rút gọn biểu thức:

a.A= (5√5 +2√45 + √5).√5

b.B= 2√2 +1/2√2-4√50

c.C=1/1-√2 + 1/1+√2

Câu 2: Tìm x, biết:

√(8-4x)²  =2

Answer 1

[Yeutoanhoc]

`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}`

Answer 2

[Trúc Giang]

\(A=\left(5\sqrt{5}+6\sqrt{5}+\sqrt{5}\right).\sqrt{5}=12\sqrt{5}.\sqrt{5}=12.5=60\)

\(B=2\sqrt{2}+\dfrac{1}{2}\sqrt{2}-10\sqrt{2}=-7,5.\sqrt{2}\)

\(C=\dfrac{1}{1-\sqrt{2}}+\dfrac{1}{1+\sqrt{2}}=\dfrac{1+\sqrt{2}}{-1}+\dfrac{1-\sqrt{2}}{-1}=-1-\sqrt{2}-1+\sqrt{2}=-2\)

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

\(\sqrt{\left(8-4x\right)^2}=2\)

\(\Leftrightarrow4x-8=2\Leftrightarrow4x=10\Leftrightarrow x=\dfrac{10}{4}=\dfrac{5}{2}\)