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18 tháng 2 2021
1) Vì x=25 thỏa mãn ĐKXĐ nên Thay x=25 vào biểu thức \(A=\dfrac{\sqrt{x}-2}{x+1}\), ta được:
\(A=\dfrac{\sqrt{25}-2}{25+1}=\dfrac{5-2}{25+1}=\dfrac{3}{26}\)
Vậy: Khi x=25 thì \(A=\dfrac{3}{26}\)
2) Ta có: \(B=\dfrac{\sqrt{x}-3}{\sqrt{x}+1}+\dfrac{2x+8\sqrt{x}-6}{x-\sqrt{x}-2}\)
\(=\dfrac{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}+\dfrac{2x+8\sqrt{x}-6}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{x-5\sqrt{x}+6+2x+8\sqrt{x}-6}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{3x+3\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{3\sqrt{x}\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{3\sqrt{x}}{\sqrt{x}-2}\)
6 tháng 5 2021
ĐKXĐ: x>0; x ≠ 1
P = \(\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-1}-\dfrac{\sqrt{x}-1}{\sqrt{x}+1}+4\sqrt{x}\right)\left(\sqrt{x}-\dfrac{1}{\sqrt{x}}\right)\)
= \(\dfrac{x+2\sqrt{x}+1-x+2\sqrt{x}-1+4x\sqrt{x}-4\sqrt{x}}{x-1}.\dfrac{x-1}{\sqrt{x}}\)
= \(\dfrac{4x\sqrt{x}}{\sqrt{x}}\)= 4x
Vậy P = 4x với x > 0; x ≠ 1
DN
2
8 tháng 11 2021
Bài 4:
\(a,A=\dfrac{x-1}{\sqrt{x}\left(\sqrt{x}-1\right)}=\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}=\dfrac{\sqrt{x}+1}{\sqrt{x}}\\ P=A:B=\dfrac{\sqrt{x}+1}{\sqrt{x}}\cdot\dfrac{x-1}{\sqrt{x}+1}=\dfrac{x-1}{\sqrt{x}}\\ b,P\sqrt{x}=m-\sqrt{x}+x\\ \Leftrightarrow x-1=m-\sqrt{x}+x\\ \Leftrightarrow m=\sqrt{x}-1\)
KT
1
19 tháng 11 2021
Vì -3<0 nên góc tạo bởi y=5-3x và Ox là góc tù
Gọi góc tạo bởi đt và Ox là \(\alpha\)
PT giao Ox: \(y=0\Leftrightarrow x=\dfrac{5}{3}\Leftrightarrow A\left(\dfrac{5}{3};0\right)\Leftrightarrow OA=\dfrac{5}{3}\)
PT giao Oy: \(x=0\Leftrightarrow y=5\Leftrightarrow B\left(0;5\right)\Leftrightarrow OB=5\)
Ta có \(\tan\left(180^0-\alpha\right)=\dfrac{OB}{OA}=5\cdot\dfrac{3}{5}=3\approx\tan72^0\)
\(\Rightarrow\alpha\approx180^0-72^0=108^0\)
Vậy ...
HN
3
12 tháng 9 2021
đề như thế này à \(\dfrac{\sqrt{27-3\sqrt{2}+2\sqrt{6}}}{3\sqrt{3}}\)
28 tháng 2 2021
`2x+5y=11(1)`
`2x-3y=0(2)`
Lấy (1) trừ (2)
`=>8y=11`
`<=>y=11/8`
`<=>x=(3y)/2=33/16`
28 tháng 2 2021
a) Ta có: \(\left\{{}\begin{matrix}2x+5y=11\\2x-3y=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}8y=11\\2x-3y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{11}{8}\\2x=3y=3\cdot\dfrac{11}{8}=\dfrac{33}{8}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{33}{16}\\y=\dfrac{11}{8}\end{matrix}\right.\)
Vậy: Hệ phương trình có nghiệm duy nhất là \(\left\{{}\begin{matrix}x=\dfrac{33}{16}\\y=\dfrac{11}{8}\end{matrix}\right.\)
b) Ta có: \(\left\{{}\begin{matrix}4x+3y=6\\2x+y=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}4x+3y=6\\4x+2y=8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-2\\2x+y=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x-2=4\\y=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=6\\y=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-2\end{matrix}\right.\)
Vậy: Hệ phương trình có nghiệm duy nhất là (x,y)=(3;-2)
NT
1
\(P=\left[\dfrac{a+3\sqrt{a}+2}{\left(\sqrt{a}+2\right)\left(\sqrt{a}-1\right)}-\dfrac{a+\sqrt{a}}{a-1}\right]:\left(\dfrac{1}{\sqrt{a}+1}+\dfrac{1}{\sqrt{a}-1}\right)\) (đk:\(a\ge0;a\ne1\))
\(=\left[\dfrac{\left(\sqrt{a}+1\right)\left(\sqrt{a}+2\right)}{\left(\sqrt{a}+2\right)\left(\sqrt{a}-1\right)}-\dfrac{\sqrt{a}\left(\sqrt{a}+1\right)}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\right]:\dfrac{\sqrt{a}-1+\sqrt{a}+1}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\)
\(=\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-1}-\dfrac{\sqrt{a}}{\sqrt{a}-1}\right).\dfrac{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}{2\sqrt{a}}\)
\(=\dfrac{1}{\sqrt{a}-1}.\dfrac{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}{2\sqrt{a}}=\dfrac{\sqrt{a}+1}{2\sqrt{a}}\)
2) \(\dfrac{1}{P}\ge\dfrac{\sqrt{a}+9}{8}\)
\(\Leftrightarrow\dfrac{2\sqrt{a}}{\sqrt{a}+1}\ge\dfrac{\sqrt{a}+9}{8}\)
\(\Leftrightarrow16\sqrt{a}\ge\left(\sqrt{a}+9\right)\left(\sqrt{a}+1\right)\)
\(\Leftrightarrow a-6\sqrt{a}+9\le0\)
\(\Leftrightarrow\left(\sqrt{a}-3\right)^2\le0\)
Dấu "=" xảy ra khi \(\sqrt{a}-3=0\Leftrightarrow a=9\) (tm)
Vậy...
1) ĐKXĐ: \(a\ge0;a\ne1\)
\(P=\left[\dfrac{a+\sqrt{a}+2\sqrt{a}+2}{\left(\sqrt{a}+2\right).\left(\sqrt{a}-1\right)}-\dfrac{\sqrt{a}.\left(\sqrt{a}+1\right)}{\left(\sqrt{a}-1\right).\left(\sqrt{a}+1\right)}\right]\)\(:\left[\dfrac{\sqrt{a}-1+\sqrt{a}+1}{\left(\sqrt{a}-1\right).\left(\sqrt{a}+1\right)}\right]\)
\(\Leftrightarrow P=\left[\dfrac{\sqrt{a}.\left(\sqrt{a}+1\right)+2.\left(\sqrt{a}+1\right)}{\left(\sqrt{a}+2\right).\left(\sqrt{a}-1\right)}-\dfrac{\sqrt{a}}{\sqrt{a}-1}\right]\)\(:\dfrac{2\sqrt{a}}{\left(\sqrt{a}-1\right).\left(\sqrt{a}+1\right)}\)
\(\Leftrightarrow P=\left[\dfrac{\left(\sqrt{a}+2\right).\left(\sqrt{a}+1\right)}{\left(\sqrt{a}+2\right).\left(\sqrt{a}-1\right)}-\dfrac{\sqrt{a}}{\sqrt{a}-1}\right].\dfrac{\left(\sqrt{a}-1\right).\left(\sqrt{a}+1\right)}{2\sqrt{a}}\)
\(\Leftrightarrow P=\dfrac{\sqrt{a}+1-\sqrt{a}}{\sqrt{a}-1}.\dfrac{\left(\sqrt{a}-1\right).\left(\sqrt{a}+1\right)}{2\sqrt{a}}\)
\(\Leftrightarrow P=\dfrac{\sqrt{a}+1}{2\sqrt{a}}\)
2) Có : \(\dfrac{1}{P}\ge\dfrac{\sqrt{a}+9}{8}\)
\(\Leftrightarrow\dfrac{2\sqrt{a}}{\sqrt{a}+1}\ge\dfrac{\sqrt{a}+9}{8}\)
\(\Leftrightarrow\dfrac{2\sqrt{a}}{\sqrt{a}+1}-\dfrac{\sqrt{a}+9}{8}\ge0\)
\(\Leftrightarrow\dfrac{16\sqrt{a}-\left(\sqrt{a}+9\right).\left(\sqrt{a}+1\right)}{8.\left(\sqrt{a}+1\right)}\ge0\)
\(\Leftrightarrow\dfrac{16\sqrt{a}-a-10\sqrt{a}-9}{8.\left(\sqrt{a}+1\right)}\ge0\)
\(\Leftrightarrow\dfrac{-\left(a-6\sqrt{a}+9\right)}{8.\left(\sqrt{a}+1\right)}\ge0\)
\(\Leftrightarrow\dfrac{\left(\sqrt{a}-3\right)^2}{8.\left(\sqrt{a}+1\right)}\le0\)
Vì \(\sqrt{a}\ge0\Rightarrow8.\left(\sqrt{a}+1\right)>0\) mà \(\left(\sqrt{a}-3\right)^2\) \(\ge0\)
\(\Rightarrow\) \(\dfrac{\left(\sqrt{a}-3\right)^2}{8.\left(\sqrt{a}+1\right)}=0\) \(\Rightarrow\left(\sqrt{a}-3\right)^2=0\) \(\Leftrightarrow\sqrt{a}-3=0\Leftrightarrow\sqrt{a}=3\Leftrightarrow a=9\)
Vậy để\(\dfrac{1}{P}\ge\dfrac{\sqrt{a}+9}{8}\) thì \(a=9\)