(sqrt(5) - 2)/(5 + 2sqrt(5)) - 1/(2 + sqrt(5)) + 1/(sqrt(5))
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TT
4
TC
1
AH
Akai Haruma
Giáo viên
9 tháng 7 2023
Bạn nên viết đề bằng công thức toán (biểu tượng $\sum$ góc trái khung soạn thảo) để mọi người hiểu đề của bạn hơn.
15 tháng 12 2023
a: \(A=\left(1-\dfrac{5+\sqrt{5}}{1+\sqrt{5}}\right)\left(\dfrac{5-\sqrt{5}}{1-\sqrt{5}}-1\right)\)
\(=\left(1-\dfrac{\sqrt{5}\left(\sqrt{5}+1\right)}{\sqrt{5}+1}\right)\left(\dfrac{-\sqrt{5}\left(1-\sqrt{5}\right)}{1-\sqrt{5}}-1\right)\)
\(=\left(1-\sqrt{5}\right)\left(-1-\sqrt{5}\right)\)
\(=\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)=5-1=4\)
b: ĐKXĐ: \(\left\{{}\begin{matrix}x>=0\\x< >1\end{matrix}\right.\)
\(B=\dfrac{1}{2\sqrt{x}-2}-\dfrac{1}{2\sqrt{x}+2}+\dfrac{\sqrt{x}}{1-x}\)
\(=\dfrac{1}{2\left(\sqrt{x}-1\right)}-\dfrac{1}{2\left(\sqrt{x}+1\right)}-\dfrac{\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{\sqrt{x}+1-\sqrt{x}+1-2\sqrt{x}}{\left(\sqrt{x}-1\right)\cdot\left(\sqrt{x}+1\right)}\)
\(=\dfrac{-2\sqrt{x}+2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=-\dfrac{2\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=-\dfrac{2}{\sqrt{x}+1}\)
c: Khi x=9 thì \(B=\dfrac{-2}{\sqrt{9}+1}=\dfrac{-2}{3+1}=-\dfrac{2}{4}=-\dfrac{1}{2}\)
d: |B|=A
=>\(\left|-\dfrac{2}{\sqrt{x}+1}\right|=4\)
=>\(\dfrac{2}{\sqrt{x}+1}=4\) hoặc \(\dfrac{2}{\sqrt{x}+1}=-4\)
=>\(\sqrt{x}+1=\dfrac{1}{2}\) hoặc \(\sqrt{x}+1=-\dfrac{1}{2}\)
=>\(\sqrt{x}=-\dfrac{1}{2}\)(loại) hoặc \(\sqrt{x}=-\dfrac{3}{2}\)(loại)
TN
2
14 tháng 5 2023
\(=\sqrt{5}-\dfrac{\sqrt{5}\left(\sqrt{5}-2\right)}{2\left(\sqrt{5}-2\right)}=\sqrt{5}-\dfrac{\sqrt{5}}{2}=\dfrac{\sqrt{5}}{2}\)
LD
14 tháng 5 2023
=√5-\(\dfrac{\text{√}5\left(\text{√}5-2\right)}{2\left(\text{√}5-2\right)}\)=√5-\(\dfrac{\text{√5}}{2}\)=\(\dfrac{\text{√ 5}}{2}\)
T
2
26 tháng 6 2023
\(=\sqrt{4\cdot\left(3-\sqrt{5}\right)^2}+2\sqrt{\left(3+\sqrt{5}\right)^2}\)
=2(3-căn 5)+2(3+căn 5)
=6-2căn 5+6+2căn 5=12
1 tháng 8 2023
1: =>x^2-x=3-x
=>x^2=3
=>x=căn 3 hoặc x=-căn 3
2: =>x^2-4x+3=x^2-4x+4 và x>=2
=>3=4(vô lý)
3: =>2|x-1|=6
=>|x-1|=3
=>x-1=3 hoặc x-1=-3
=>x=-2 hoặc x=4
4: =>|2x-3|=|x-2|
=>2x-3=x-2 hoặc 2x-3=-x+2
=>x=1 hoặc x=5/3
5: =>\(\sqrt{x+2}\left(\sqrt{x-2}+\sqrt{x+2}\right)=0\)
=>x+2=0
=>x=-2
DT
2
29 tháng 10 2023
\(\dfrac{1}{\sqrt{5}-\sqrt{3}}+\dfrac{5\sqrt{3}-3\sqrt{5}}{2\sqrt{15}-\sqrt{20}}\)
\(=\dfrac{1}{\sqrt{5}-\sqrt{3}}+\dfrac{5\sqrt{3}-3\sqrt{5}}{2\left(\sqrt{15}-\sqrt{5}\right)}\)
\(=\dfrac{2\sqrt{15}-2\sqrt{5}+\sqrt{15}\left(8-2\sqrt{15}\right)}{2\sqrt{5}\left(\sqrt{3}-1\right)\left(\sqrt{5}-\sqrt{3}\right)}\)
\(=\dfrac{2\sqrt{15}-2\sqrt{5}+8\sqrt{15}-30}{2\sqrt{5}\left(\sqrt{3}-1\right)\left(\sqrt{5}-\sqrt{3}\right)}\)
\(=\dfrac{10\sqrt{15}-2\sqrt{5}-30}{2\sqrt{5}\left(\sqrt{3}-1\right)\left(\sqrt{5}-\sqrt{3}\right)}\)
\(=\dfrac{2\sqrt{5}\left(5\sqrt{3}-1-3\sqrt{5}\right)}{2\sqrt{5}\left(\sqrt{3}-1\right)\left(\sqrt{5}-\sqrt{3}\right)}=\dfrac{5\sqrt{3}-3\sqrt{5}-1}{\left(\sqrt{3}-1\right)\left(\sqrt{5}-\sqrt{3}\right)}\)
H9
HT.Phong (9A5)
CTVHS
29 tháng 10 2023
\(\dfrac{1}{\sqrt{5}-\sqrt{3}}+\dfrac{5\sqrt{3}-3\sqrt{5}}{2\sqrt{15}-\sqrt{20}}\)
\(=\dfrac{\sqrt{5}+\sqrt{3}}{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}+\dfrac{\sqrt{15}\left(\sqrt{5}-\sqrt{3}\right)}{2\sqrt{5}\left(\sqrt{3}-1\right)}\)
\(=\dfrac{\sqrt{5}+3}{5-3}+\dfrac{\sqrt{3}\left(\sqrt{5}-\sqrt{3}\right)}{2\left(\sqrt{3}-1\right)}\)
\(=\dfrac{\sqrt{5}+\sqrt{3}}{2}+\dfrac{\left(\sqrt{15}-3\right)\left(\sqrt{3}+1\right)}{2\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}\)
\(=\dfrac{\sqrt{5}+\sqrt{3}}{2}+\dfrac{3\sqrt{5}+\sqrt{15}-3\sqrt{3}-3}{2\cdot2}\)
\(=\dfrac{2\sqrt{5}+2\sqrt{3}+3\sqrt{5}+\sqrt{15}-3\sqrt{3}-3}{4}\)
\(=\dfrac{5\sqrt{5}-\sqrt{3}+\sqrt{15}-3}{4}\)
H9
HT.Phong (9A5)
CTVHS
26 tháng 9 2023
a) \(4\sqrt{2x+1}-\sqrt{8x+4}+\dfrac{1}{2}\sqrt{32x+16}=12\) (ĐK: \(x\ge-\dfrac{1}{2}\))
\(\Leftrightarrow4\sqrt{2x+1}-\sqrt{4\left(2x+1\right)}+\dfrac{1}{2}\cdot4\sqrt{2x+1}=12\)
\(\Leftrightarrow4\sqrt{2x+1}-2\sqrt{2x+1}+2\sqrt{2x+1}=12\)
\(\Leftrightarrow4\sqrt{2x+1}=12\)
\(\Leftrightarrow\sqrt{2x+1}=\dfrac{12}{4}\)
\(\Leftrightarrow2x+1=3^2\)
\(\Leftrightarrow2x=9-1\)
\(\Leftrightarrow2x=8\)
\(\Leftrightarrow x=\dfrac{8}{2}\)
\(\Leftrightarrow x=4\left(tm\right)\)
b) \(\sqrt{4x^2-4x+1}=5\)
\(\Leftrightarrow\sqrt{\left(2x-1\right)^2}=5\)
\(\Leftrightarrow\left|2x-1\right|=5\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-1=5\left(x\ge\dfrac{1}{2}\right)\\2x-1=-5\left(x< \dfrac{1}{2}\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=6\\2x=-4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{6}{2}\\x=-\dfrac{4}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\left(tm\right)\\x=-2\left(tm\right)\end{matrix}\right.\)
c) \(\dfrac{2\sqrt{x}-3}{\sqrt{x}-1}=-\dfrac{1}{2}\)(ĐK: \(x\ge0;x\ne1\))
\(\Leftrightarrow-\left(\sqrt{x}-1\right)=2\left(2\sqrt{x}-3\right)\)
\(\Leftrightarrow-\sqrt{x}+1=4\sqrt{x}-6\)
\(\Leftrightarrow4\sqrt{x}+\sqrt{x}=1+6\)
\(\Leftrightarrow5\sqrt{x}=7\)
\(\Leftrightarrow\sqrt{x}=\dfrac{7}{5}\)
\(\Leftrightarrow x=\dfrac{49}{25}\left(tm\right)\)
\(=\dfrac{-20+9\sqrt{5}}{5}-\dfrac{\sqrt{5}-2}{1}+\dfrac{\sqrt{5}}{5}\)
\(=-4+2\sqrt{5}-\sqrt{5}+2=-2+\sqrt{5}\)