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a) \(\dfrac{\sqrt{16a^4b^6}}{\sqrt{128a^6b^6}}\)
\(=\dfrac{4a^2b^3}{8\sqrt{2}a^3b^3}\)
\(=\dfrac{1}{2\sqrt{2}a}\)
\(=\dfrac{\sqrt{2}}{4a}\)
b) \(\sqrt{\dfrac{x-2\sqrt{x}+1}{x+2\sqrt{x}+1}}\)
chịu đấy :v
c) \(\sqrt{\dfrac{\left(x-2\right)^2}{\left(3-x\right)^2}}+\dfrac{x^2-1}{x-3}\)
\(=\dfrac{x-2}{3-x}+\dfrac{x^2-1}{x-3}\)
\(=\dfrac{x-2}{-\left(x-3\right)}+\dfrac{x^2-1}{x-3}\)
\(=-\dfrac{x-2}{x-3}+\dfrac{x^2-1}{x-3}\)
\(=\dfrac{-\left(x-2\right)+x^2-1}{x-3}\)
\(=\dfrac{-x+1+x^2}{x-3}\)
d) \(\dfrac{x-1}{\sqrt{y}-1}\cdot\sqrt{\dfrac{\left(y-2\sqrt{y}+1^2\right)}{\left(x-1\right)^4}}\)
\(=\dfrac{x-1}{\sqrt{y}-1}\cdot\sqrt{\dfrac{y-2\sqrt{y}+1}{\left(x-1\right)^4}}\)
\(=\dfrac{x-1}{\sqrt{y}-1}\cdot\dfrac{\sqrt{y-2\sqrt{y}+1}}{\left(x-1\right)^2}\)
\(=\dfrac{1}{\sqrt{y}-1}\cdot\dfrac{\sqrt{y-2\sqrt{y}+1}}{x-1}\)
\(=\dfrac{\sqrt{y-2\sqrt{y}+1}}{\left(\sqrt{y}-1\right)\left(x-1\right)}\)
\(=\dfrac{\sqrt{y-2\sqrt{y}+1}}{x\sqrt{y}-\sqrt{y}-x+1}\)
e) \(4x-\sqrt{8}+\dfrac{\sqrt{x^3+2x^2}}{\sqrt{x+2}}\)
\(=4x-2\sqrt{2}+\dfrac{\sqrt{x^2\cdot\left(x+2\right)}}{\sqrt{x+2}}\)
\(=4x-2\sqrt{2}+\sqrt{x^2}\)
\(=4x-2\sqrt{x}+x\)
\(=5x-2\sqrt{2}\)
HD nha bn^^
\(x\sqrt{x}-1=\sqrt{x^3}-1\) (Hằng đẳng thức)
Mấu chốt là ở chỗ này. Bn khai triển sau rút gọn là đc
mk giải 1 bài lm mẩu nha .
+) ta có : \(A=x-12\sqrt{x}\Leftrightarrow x-12\sqrt{x}-A=0\)
vì phương trình này luôn có nghiệm \(\Leftrightarrow\Delta'\ge0\)
\(\Leftrightarrow6^2+A\ge0\Leftrightarrow A\ge-36\)
vậy giá trị nhỏ nhất của \(A\) là \(-36\) dấu "=" xảy ra khi \(\sqrt{x}=\dfrac{-b'}{a}=\dfrac{6}{1}=6\Leftrightarrow x=36\)
mấy câu còn lại bn chuyển quế đưa về phương trình bật 2 theo \(x\) rồi giải như trên là đc :
lộn ! là phương trình bật 2 đối với ẩn là \(\sqrt{x}\) nha :
DƯƠNG PHAN KHÁNH DƯƠNG
2. \(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{\left(2+\sqrt{3}\right)^2}}}}=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\left(2+\sqrt{3}\right)}}}=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-20-10\sqrt{3}}}}=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{28-10\sqrt{3}}}}=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{\left(5-\sqrt{3}\right)^2}}}=\)
\(\sqrt{4+\sqrt{5\sqrt{3}+25-5\sqrt{3}}}=\sqrt{4+\sqrt{25}}=\sqrt{4+5}=3\)
3. Ta có: VT=\(\left(\dfrac{1-a\sqrt{a}}{1-\sqrt{a}}:\sqrt{a}\right).\left(\dfrac{1-\sqrt{a}}{1-a}\right)=\left[\dfrac{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}+a\right)}{1-\sqrt{a}}.\dfrac{1}{\sqrt{a}}\right].\left[\dfrac{1-\sqrt{a}}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)}\right]=\dfrac{1+\sqrt{a}+a}{\sqrt{a}}.\dfrac{1}{1+\sqrt{a}}=\dfrac{1+\sqrt{a}+a}{\sqrt{a}+a}=\dfrac{1}{\sqrt{a}+a}+1\)
??? Sao rút gọn rồi ra kì vậy nhờ =="
1,
a.
\(\left[{}\begin{matrix}x-5\sqrt{x}+6\ne0\\\sqrt{x}-2\ne0\\3-\sqrt{x}\ne0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)\ne0\\\sqrt{x}\ne2\\\sqrt{x}\ne3\end{matrix}\right.\)
\(\left[{}\begin{matrix}\sqrt{x}\ne3\\\sqrt{x}\ne2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x\ne9\\x\ne4\end{matrix}\right.\)
Vậy ĐKXĐ : \(\left[{}\begin{matrix}x\ne9\\x\ne4\end{matrix}\right.\)
a) \(13-\sqrt{\left(8x-1\right)^2}=\sqrt{x^2}\) (*)
\(\Leftrightarrow13-\left|8x-1\right|=\left|x\right|\)
Th1: \(8x-1\ge0\Leftrightarrow x\ge\dfrac{1}{8}\)
(*) \(\Leftrightarrow13-8x+1=x\Leftrightarrow9x=14\Leftrightarrow x=\dfrac{14}{9}\left(N\right)\)
Th2: \(x\le0\)
(*) \(\Leftrightarrow13+8x-1=-x\Leftrightarrow9x=-12\Leftrightarrow x=-\dfrac{4}{3}\left(N\right)\)
Th3: \(\left\{{}\begin{matrix}8x-1\ge0\\x\le0\end{matrix}\right.\Leftrightarrow\dfrac{1}{8}\le x\le0\) (vô lý)
Th4: \(\left\{{}\begin{matrix}8x-1\le0\\x\ge0\end{matrix}\right.\Leftrightarrow0\le x\le\dfrac{1}{8}\)
(*) \(\Leftrightarrow13-8x+1=x\Leftrightarrow9x=14\Leftrightarrow x=\dfrac{14}{9}\left(L\right)\)
Kl: x= 14/9 , x= -4/3
b) \(\sqrt{\left(x+1\right)^2}+\sqrt{\left(2x+3\right)^2}=3\Leftrightarrow\left|x+1\right|+\left|2x+3\right|=3\)(*)
Th1: \(x\ge-1\)
(*) \(\Leftrightarrow x+1+2x+3=3\Leftrightarrow3x=-1\Leftrightarrow x=-\dfrac{1}{3}\left(N\right)\)
Th2: \(x\le-\dfrac{3}{2}\)
(*) \(\Leftrightarrow-x-1-2x-3=3\Leftrightarrow-3x=7\Leftrightarrow x=-\dfrac{7}{3}\left(N\right)\)
Th3: \(\left\{{}\begin{matrix}x+1\ge0\\2x+3\le0\end{matrix}\right.\Leftrightarrow-1\le x\le-\dfrac{3}{2}\) (vô lý)
Th4: \(\left\{{}\begin{matrix}x+1\le0\\2x+3\ge0\end{matrix}\right.\Leftrightarrow-\dfrac{3}{2}\le x\le-1\)
(*) \(\Leftrightarrow-x-1-2x-3=3\Leftrightarrow-3x=7\Leftrightarrow x=-\dfrac{7}{3}\left(L\right)\)
Kl: x= -1/3 , x= -7/3
a: \(A=\dfrac{-\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}{\sqrt{x}+3}-\dfrac{\left(\sqrt{x}-3\right)^2}{\sqrt{x}-3}-6\)
\(=-\sqrt{x}+3-\sqrt{x}+3-6=-2\sqrt{x}\)
b: \(\left(\dfrac{2\sqrt{x}}{x\sqrt{x}+x+\sqrt{x}+1}-\dfrac{1}{\sqrt{x}+1}\right):\left(\dfrac{2\sqrt{x}}{\sqrt{x}+1}-1\right)\)
\(=\left(\dfrac{2\sqrt{x}}{\left(\sqrt{x}+1\right)\left(x+1\right)}-\dfrac{1}{\sqrt{x}+1}\right):\dfrac{2\sqrt{x}-\sqrt{x}-1}{\sqrt{x}+1}\)
\(=\dfrac{2\sqrt{x}-x-1}{\left(\sqrt{x}+1\right)\left(x+1\right)}\cdot\dfrac{\sqrt{x}+1}{\sqrt{x}-1}=\dfrac{1}{x+1}\)
g: \(\left(\dfrac{1}{\sqrt{x}-1}+\dfrac{1}{\sqrt{x}+1}\right)\left(\dfrac{x-1}{\sqrt{x}+1}-2\right)\)
\(=\dfrac{\sqrt{x}+1+\sqrt{x}-1}{x-1}\cdot\left(\sqrt{x}-1-2\right)\)
\(=\dfrac{2\sqrt{x}\left(\sqrt{x}-3\right)}{x-1}\)
Câu 1:
a: \(P=\dfrac{a-4-5-\sqrt{a}-3}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-2\right)}\)
\(=\dfrac{a-\sqrt{a}-12}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-2\right)}=\dfrac{\sqrt{a}-4}{\sqrt{a}-2}\)
b: Để P<1 thì \(\dfrac{\sqrt{a}-4-\sqrt{a}+2}{\sqrt{a}-2}< 0\)
\(\Leftrightarrow\sqrt{a}-2< 0\)
hay 0<a<4
ĐKXĐ : \(x\ge0\) và \(x\ne\dfrac{1}{9}\)
\(\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{3\sqrt{x}-1}=\dfrac{6}{5}\)
\(\Leftrightarrow\dfrac{5\sqrt{x}\left(\sqrt{x}+1\right)}{5\left(3\sqrt{x}-1\right)}=\dfrac{6\left(3\sqrt{x}-1\right)}{5\left(3\sqrt{x}-1\right)}\)
\(\Leftrightarrow5\sqrt{x}\left(\sqrt{x}+1\right)=6\left(3\sqrt{x}-1\right)\)
\(\Leftrightarrow5x+5\sqrt{x}-18\sqrt{x}+6=0\)
\(\Leftrightarrow5x-13\sqrt{x}+6=0\)
\(\Leftrightarrow5x-10\sqrt{x}-3\sqrt{x}+6=0\)
\(\Leftrightarrow5\sqrt{x}\left(\sqrt{x}-2\right)-3\left(\sqrt{x}-2\right)=0\)
\(\Leftrightarrow\left(\sqrt{x}-2\right)\left(5\sqrt{x}-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}-2=0\\5\sqrt{x}-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=\dfrac{9}{25}\end{matrix}\right.\)
Vậy \(S=\left\{\dfrac{9}{25};4\right\}\)
Học tốt !