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28 tháng 5 2019
\(M=\left(\frac{\sqrt{x}}{x-36}-\frac{\sqrt{x}-6}{x+6\sqrt{x}}\right):\frac{2\sqrt{x}-6}{x+6\sqrt{x}}\)
=\(\left(\frac{\sqrt{x}}{\left(\sqrt{x}\right)^2-6^2}-\frac{\sqrt{x}-6}{\sqrt{x}\left(\sqrt{x}+6\right)}\right):\frac{2\sqrt{x}-6}{\sqrt{x}\left(\sqrt{x}+6\right)}\)
=\(\left(\frac{\sqrt{x}}{\left(\sqrt{x}-6\right)\left(\sqrt{x}+6\right)}-\frac{\sqrt{x}-6}{\sqrt{x}\left(\sqrt{x}+6\right)}\right).\frac{\sqrt{x}\left(\sqrt{x}+6\right)}{2\sqrt{x}-6}\)
=\(\left(\frac{x-\left(\sqrt{x}-6\right)\left(\sqrt{x}+6\right)}{\sqrt{x}\left(\sqrt{x}-6\right)\left(\sqrt{x}+6\right)}\right).\frac{\sqrt{x}\left(\sqrt{x}+6\right)}{2\sqrt{x}-6}\)
=\(\left(\frac{x-x+6\sqrt{x}+6\sqrt{x}-36}{\sqrt{x}\left(\sqrt{x}-6\right)\left(\sqrt{x}+6\right)}\right).\frac{\sqrt{x}\left(\sqrt{x}+6\right)}{2\sqrt{x}-6}\)
=\(\left(\frac{12\sqrt{x}-36}{\sqrt{x}\left(\sqrt{x}-6\right)\left(\sqrt{x}+6\right)}\right).\frac{\sqrt{x}\left(\sqrt{x}+6\right)}{2\sqrt{x}-6}\)
=\(\left(\frac{12\left(\sqrt{x}-3\right)}{\sqrt{x}\left(\sqrt{x}-6\right)\left(\sqrt{x}+6\right)}\right).\frac{\sqrt{x}\left(\sqrt{x}+6\right)}{2\left(\sqrt{x}-3\right)}\)
=\(\frac{6}{\sqrt{x}-6}\)
TN
0
AH
Akai Haruma
Giáo viên
5 tháng 4 2018
Lời giải:
ĐKXĐ: \(x\neq -3; x\neq \pm 6; x\neq 0\)
Ta có:
\(A=\left(\frac{x}{x^2-36}-\frac{x+6}{x^2-6x}\right): \frac{2x+6}{x^2-6x}-\frac{x}{x+6}\)
\(A=\left(\frac{x}{x^2-36}-\frac{x+6}{x^2-6x}\right).\frac{x^2-6x}{2x+6}-\frac{x}{x+6}\)
\(=\frac{x(x^2-6x)}{(x^2-36)(2x+6)}-\frac{(x+6)(x^2-6x)}{x^2-6x)(2x+6)}-\frac{x}{x+6}\)
\(=\frac{x^2(x-6)}{(x-6)(x+6)(2x+6)}-\frac{x+6}{2x+6}-\frac{x}{x+6}\)
\(=\frac{x^2}{(x+6)(2x+6)}-\frac{(x+6)^2}{(2x+6)(x+6)}-\frac{x(2x+6)}{(2x+6)(x+6)}\)
\(=\frac{x^2-(x+6)^2-x(2x+6)}{(x+6)(2x+6)}=\frac{-(2x^2+18x+36)}{2x^2+18x+36}=-1\)
3 tháng 7 2020
a) ĐKXĐ: \(\left\{{}\begin{matrix}x\ge0\\x-36\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x\ne36\end{matrix}\right.\)
b) Ta có: \(A=\left(\frac{\sqrt{x}}{x-36}-\frac{\sqrt{x}-6}{x+6\sqrt{x}}\right):\frac{2\sqrt{x}-6}{x+6\sqrt{x}}+\frac{\sqrt{x}}{6-\sqrt{x}}\)
\(=\left(\frac{x}{\sqrt{x}\left(\sqrt{x}+6\right)\left(\sqrt{x}-6\right)}-\frac{\left(\sqrt{x}-6\right)^2}{\sqrt{x}\left(\sqrt{x}+6\right)\left(\sqrt{x}-6\right)}\right)\cdot\frac{\sqrt{x}\left(\sqrt{x}+6\right)}{2\left(\sqrt{x}-3\right)}+\frac{\sqrt{x}}{6-\sqrt{x}}\)
\(=\frac{12\left(\sqrt{x}-3\right)}{\sqrt{x}\left(\sqrt{x}+6\right)\left(\sqrt{x}-6\right)}\cdot\frac{\sqrt{x}\left(\sqrt{x}+6\right)}{2\left(\sqrt{x}-3\right)}-\frac{\sqrt{x}}{\sqrt{x}-6}\)
\(=\frac{6}{\sqrt{x}-6}-\frac{\sqrt{x}}{\sqrt{x}-6}=\frac{6-\sqrt{x}}{-\left(6-\sqrt{x}\right)}=\frac{1}{-1}=-1\)
Vậy: Biểu thức \(A=\left(\frac{\sqrt{x}}{x-36}-\frac{\sqrt{x}-6}{x+6\sqrt{x}}\right):\frac{2\sqrt{x}-6}{x+6\sqrt{x}}+\frac{\sqrt{x}}{6-\sqrt{x}}\) không phụ thuộc vào x, với \(\left\{{}\begin{matrix}x\ge0\\x\ne36\end{matrix}\right.\)
3 tháng 12 2017
5 .\(\frac{x}{\sqrt{2\left(y^2+z^2\right)-x^2}}=\frac{\sqrt{3}x^2}{\sqrt{3}x\sqrt{2\left(y^2+z^2\right)-x^2}}\ge\frac{\sqrt{3}x^2}{x^2+y^2+z^2}\)
TT=>VT2>=VP2
6.\(1+\sqrt{y-1}\ge1\)
\(\frac{1}{y^2}-\left(x+z\right)^2\le1\)
=>VT1>=VP1
10b pt1\(\Leftrightarrow\left(y-3x\right)\left(y^2-y+1\right)=0\)
NV
Nguyễn Việt Lâm
Giáo viên
6 tháng 8 2021
1.
ĐKXĐ: \(x< 5\)
\(\Leftrightarrow\sqrt{\dfrac{42}{5-x}}-3+\sqrt{\dfrac{60}{7-x}}-3=0\)
\(\Leftrightarrow\dfrac{\dfrac{42}{5-x}-9}{\sqrt{\dfrac{42}{5-x}}+3}+\dfrac{\dfrac{60}{7-x}-9}{\sqrt{\dfrac{60}{7-x}}+3}=0\)
\(\Leftrightarrow\dfrac{9x-3}{\left(5-x\right)\left(\sqrt{\dfrac{42}{5-x}}+3\right)}+\dfrac{9x-3}{\left(7-x\right)\left(\sqrt{\dfrac{60}{7-x}}+3\right)}=0\)
\(\Leftrightarrow\left(9x-3\right)\left(\dfrac{1}{\left(5-x\right)\left(\sqrt{\dfrac{42}{5-x}}+3\right)}+\dfrac{1}{\left(7-x\right)\left(\sqrt{\dfrac{60}{7-x}}+3\right)}\right)=0\)
\(\Leftrightarrow x=\dfrac{1}{3}\)
NV
Nguyễn Việt Lâm
Giáo viên
6 tháng 8 2021
b.
ĐKXĐ: \(x\ge2\)
\(\sqrt{\left(x-2\right)\left(x-1\right)}+\sqrt{x+3}=\sqrt{x-2}+\sqrt{\left(x-1\right)\left(x+3\right)}\)
\(\Leftrightarrow\sqrt{\left(x-2\right)\left(x-1\right)}-\sqrt{x-2}+\sqrt{x+3}-\sqrt{\left(x-1\right)\left(x+3\right)}=0\)
\(\Leftrightarrow\sqrt{x-2}\left(\sqrt{x-1}-1\right)-\sqrt{x+3}\left(\sqrt{x-1}-1\right)=0\)
\(\Leftrightarrow\left(\sqrt{x-1}-1\right)\left(\sqrt{x-2}-\sqrt{x+3}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-1}-1=0\\\sqrt{x-2}-\sqrt{x+3}=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=1\\x-2=x+3\left(vn\right)\end{matrix}\right.\)
\(\Rightarrow x=2\)
NT
1
2 tháng 8 2017
(x+2)(x+1)(x-3)(x+6)=-36
<=>(x2+3x+2)(x2+3x-18)=-36
Đặt x2+3x+2=a =>a(a-20)+36=0
<=>(a-2)(a-18)=0
<=>\(\orbr{\begin{cases}a=2\\a=18\end{cases}}\)
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