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29 tháng 8 2021
Bài 18:
a: Ta có: \(P=\left(\dfrac{\sqrt{a}}{2}-\dfrac{1}{2\sqrt{a}}\right)^2\cdot\left(\dfrac{\sqrt{a}-1}{\sqrt{a}+1}-\dfrac{\sqrt{a}+1}{\sqrt{a}-1}\right)\)
\(=\dfrac{\left(\sqrt{a}-1\right)^2\cdot\left(\sqrt{a}+1\right)^2}{4a}\cdot\dfrac{a-2\sqrt{a}+1-a-2\sqrt{a}-1}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\)
\(=\dfrac{\left(a-1\right)\cdot\left(-4\right)\cdot\sqrt{a}}{4a}\)
\(=\dfrac{-a+1}{\sqrt{a}}\)
b: Để P<0 thì -a+1<0
\(\Leftrightarrow-a< -1\)
hay a>1
c: Để P=-2 thì \(-a+1=-2\sqrt{a}\)
\(\Leftrightarrow-a+1+2\sqrt{a}=0\)
\(\Leftrightarrow a-2\sqrt{a}+1=2\)
\(\Leftrightarrow\left(\sqrt{a}-1\right)^2=2\)
\(\Leftrightarrow\sqrt{a}-1=\sqrt{2}\)
hay \(a=3+2\sqrt{2}\)
29 tháng 8 2021
Bài 17:
a: Ta có: \(P=\dfrac{a\sqrt{a}-1}{a-\sqrt{a}}-\dfrac{a\sqrt{a}+1}{a+\sqrt{a}}+\left(\sqrt{a}-\dfrac{1}{\sqrt{a}}\right)\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-1}+\dfrac{\sqrt{a}-1}{\sqrt{a}+1}\right)\)
\(=\dfrac{a+\sqrt{a}+1-a+\sqrt{a}-1}{\sqrt{a}}+\dfrac{a-1}{\sqrt{a}}\cdot\dfrac{a+2\sqrt{a}+1+a-2\sqrt{a}+1}{a-1}\)
\(=2+\dfrac{2a+2}{\sqrt{a}}\)
\(=\dfrac{2a+2\sqrt{a}+2}{\sqrt{a}}\)
24 tháng 7 2021
Bài 3:
a) Thay x=9 vào A, ta được:
\(A=\dfrac{3+2}{3-5}=\dfrac{5}{-2}=\dfrac{-5}{2}\)
b) Ta có: M=B:A
\(=\left(\dfrac{x+3\sqrt{x}}{x-25}+\dfrac{1}{\sqrt{x}-5}\right):\dfrac{\sqrt{x}+2}{\sqrt{x}-5}\)
\(=\dfrac{x+3\sqrt{x}+\sqrt{x}+5}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}\cdot\dfrac{\sqrt{x}-5}{\sqrt{x}+2}\)
\(=\dfrac{x+4\sqrt{x}+5}{x+7\sqrt{x}+10}\)
8 tháng 7 2021
Bài 1:
a) \(\sqrt{50}=5\sqrt{2}\)
b) \(\sqrt{1210}=11\sqrt{10}\)
c) \(\sqrt{450}=15\sqrt{2}\)
d) \(\sqrt{98a^3}=7\left|a\right|\sqrt{2a}\)
e) \(\sqrt{72a^2b^3}=6\left|ab\right|\sqrt{2b}\)
f) \(\sqrt{0.27a^4b^2c}=\dfrac{3\sqrt{3}}{10}\cdot a^2\cdot\left|b\right|\cdot\sqrt{c}\)
8 tháng 7 2021
Bài 2:
a) Ta có: \(2\sqrt{48}+4\sqrt{300}-\sqrt{72}+3\sqrt{8}\)
\(=8\sqrt{3}+40\sqrt{3}-6\sqrt{2}+6\sqrt{2}\)
\(=48\sqrt{3}\)
b) Ta có: \(\left(3\sqrt{5}+\sqrt{20}\right)\cdot\left(\sqrt{24}-\sqrt{96}\right)\)
\(=5\sqrt{5}\cdot\left(-2\sqrt{6}\right)\)
\(=-10\sqrt{30}\)
c) Ta có: \(\sqrt{4.9}\cdot\sqrt{40}\cdot3\sqrt{a^2}\)
\(=\sqrt{196}\cdot3\cdot\left|a\right|\)
\(=42\left|a\right|\)
d) Ta có: \(2.2\sqrt{200}+0.06\sqrt{80000}\)
\(=2.2\cdot10\sqrt{2}+0.06\cdot200\sqrt{2}\)
\(=22\sqrt{2}+12\sqrt{2}\)
\(=34\sqrt{2}\)
PM
3
9 tháng 9 2021
Bài 1:
a: \(\sqrt{0.49a^2}=-0.7a\)
b: \(\sqrt{25\left(a-7\right)^2}=5a-35\)
c: \(\sqrt{a^4\left(a-2\right)^2}=a^2\cdot\left(a-2\right)\)
d: \(\dfrac{1}{a-3b}\cdot\sqrt{a^6\left(a-3b\right)^2}\)
\(=\dfrac{1}{a-3b}\cdot a^3\cdot\left(a-3b\right)=a^3\)
9 tháng 9 2021
Bài 2:
a: \(2\left(x+y\right)\cdot\sqrt{\dfrac{1}{x^2+2xy+y^2}}\)
\(=2\left(x+y\right)\cdot\dfrac{1}{x+y}\)
=2
b: \(\dfrac{3x}{7y}\cdot\sqrt{\dfrac{49y^2}{9x^2}}\)
\(=\dfrac{3x}{7y}\cdot\dfrac{-7y}{3x}\)
=-1
PM
1
13 tháng 9 2021
\(1,\\ a,=\dfrac{\left(3+2\sqrt{3}\right)\sqrt{3}}{3}+\dfrac{\left(2+\sqrt{2}\right)\left(\sqrt{2}-1\right)}{1}\\ =\dfrac{3\sqrt{3}+6}{3}+\sqrt{2}=\sqrt{3}+1+\sqrt{2}\\ b,=\left(\dfrac{\sqrt{5}+\sqrt{2}}{3}-\dfrac{\sqrt{5}-\sqrt{2}}{3}+1\right)\cdot\dfrac{1}{\left(\sqrt{2}+1\right)^2}\\ =\dfrac{\sqrt{5}+\sqrt{2}-\sqrt{5}+\sqrt{2}+3}{3}\cdot\dfrac{1}{\left(\sqrt{2}+1\right)^2}\\ =\dfrac{2\sqrt{2}+3}{3\left(3+2\sqrt{2}\right)}=\dfrac{1}{3}\)
\(2,\\ A=2x+\sqrt{\left(x-3\right)^2}=2x+\left|x-3\right|\\ =2\left(-5\right)+\left|-5-3\right|=-10+8=-2\\ B=\dfrac{\sqrt{\left(2x+1\right)^2}}{\left(x-4\right)\left(x+4\right)}\left(x-4\right)^2=\dfrac{\left|2x+1\right|\left(x-4\right)}{x+4}\\ B=\dfrac{17\cdot4}{12}=\dfrac{17}{3}\)
\(a,\Leftrightarrow3m-2+m-2=2\\ \Leftrightarrow m=\dfrac{3}{2}\\ b,\text{PT giao Ox: }y=0\Leftrightarrow x=\dfrac{2-m}{3m-2}\Leftrightarrow OA=\left|\dfrac{m-2}{3m-2}\right|\\ \text{PT giao Oy: }x=0\Leftrightarrow y=m-2\Leftrightarrow OB=\left|m-2\right|\\ \Leftrightarrow S_{AOB}=\dfrac{1}{2}OA\cdot OB=\dfrac{1}{2}\cdot\left|\dfrac{m-2}{3m-2}\cdot\left(m-2\right)\right|=\dfrac{1}{2}\\ \Leftrightarrow\dfrac{\left(m-2\right)^2}{\left|3m-2\right|}=1\\ \Leftrightarrow\left|3m-2\right|=\left(m-2\right)^2\Leftrightarrow\left[{}\begin{matrix}3m-2=m^2-4m+4\left(m\ge\dfrac{2}{3}\right)\\2-3m=m^2-4m+4\left(m< \dfrac{2}{3}\right)\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}m^2-7m+6=0\left(m\ge\dfrac{2}{3}\right)\\m^2-m+2=0\left(vn\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}m=1\\m=6\end{matrix}\right.\)
kbt thì ko cần ghi v đâu nha
bt thì ghi đáp án