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TN
2
1 tháng 1 2022
\(\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}}\right):\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-2}-\dfrac{\sqrt{a}+2}{\sqrt{a}-1}\right)\)
\(=\left(\dfrac{\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}-\dfrac{\sqrt{a}-1}{\sqrt{a}\left(\sqrt{a}-1\right)}\right):\left(\dfrac{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}{\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)}-\dfrac{\left(\sqrt{a}+2\right)\left(\sqrt{a}-2\right)}{\left(\sqrt{a}-1\right)\left(\sqrt{a}-2\right)}\right)\)
\(=\dfrac{\sqrt{a}-\sqrt{a}+1}{\sqrt{a}\left(\sqrt{a}-1\right)}:\left(\dfrac{a-1}{\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)}-\dfrac{a-4}{\left(\sqrt{a}-1\right)\left(\sqrt{a}-2\right)}\right)\)
\(=\dfrac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}:\dfrac{a-1-a+4}{\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)}\)
\(=\dfrac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}:\dfrac{3}{\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)}\)
\(=\dfrac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}.\dfrac{\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)}{3}\)
\(=\dfrac{\sqrt{a}-2}{3\sqrt{a}}\)
4 tháng 10 2021
\(2,\\ a,x=36\Leftrightarrow P=\dfrac{6+1}{6-2}=\dfrac{7}{4}\\ b,x=6-2\sqrt{5}\Leftrightarrow\sqrt{x}=\sqrt{5}-1\\ \Leftrightarrow P=\dfrac{\sqrt{5}-1+1}{\sqrt{5}-1-2}=\dfrac{\sqrt{5}}{\sqrt{5}-3}=\dfrac{5-3\sqrt{5}}{2}\\ c,x=\dfrac{2}{2+\sqrt{3}}=4-2\sqrt{3}\Leftrightarrow\sqrt{x}=\sqrt{3}-1\\ \Leftrightarrow P=\dfrac{\sqrt{3}-1+1}{\sqrt{3}-1-2}=\dfrac{\sqrt{3}}{\sqrt{3}-3}=\dfrac{3\left(\sqrt{3}+1\right)}{-6}=\dfrac{-\sqrt{3}-1}{2}\)
8 tháng 10 2021
\(k,=\dfrac{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)+5\left(\sqrt{a}-\sqrt{b}\right)}{\sqrt{a}+\sqrt{b}+5}\\ =\dfrac{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}+5\right)}{\sqrt{a}+\sqrt{b}+5}=\sqrt{a}-\sqrt{b}\)
8 tháng 10 2021
\(h,=\dfrac{1}{2a-1}\sqrt{25a^2\left(a^2-4a+4\right)}=\dfrac{1}{2a-1}\sqrt{25a^2\left(a-2\right)^2}\\ =\dfrac{\left|5a\left(a-2\right)\right|}{2a-1}=\left[{}\begin{matrix}\dfrac{5a\left(a-2\right)}{2a-1}\left(a\ge2;a\ne\dfrac{1}{2}\right)\\\dfrac{5a\left(2-a\right)}{2a-1}\left(0\le a< 2;a\ne\dfrac{1}{2}\right)\\\dfrac{-5a\left(2-a\right)}{2a-1}\left(a< 0\right)\end{matrix}\right.\)
19 tháng 8 2021
a: Ta có: \(\sqrt{75}-\sqrt{5\dfrac{1}{3}}+\dfrac{9}{2}\sqrt{2\dfrac{2}{3}}+2\sqrt{27}\)
\(=5\sqrt{3}+\dfrac{4}{3}\sqrt{3}+3\sqrt{6}+6\sqrt{3}\)
\(=\dfrac{37}{3}\sqrt{3}+3\sqrt{6}\)
c: Ta có: \(\left(\sqrt{12}+2\sqrt{27}\right)\cdot\dfrac{\sqrt{3}}{2}-\sqrt{150}\)
\(=\left(2\sqrt{3}+6\sqrt{3}\right)\cdot\dfrac{\sqrt{3}}{2}-5\sqrt{6}\)
\(=12-5\sqrt{6}\)
16 tháng 7 2021
Bài 2:
d) Ta có: \(\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}\)
\(=\sqrt{5}+1+\sqrt{5}-1\)
\(=2\sqrt{5}\)
e) Ta có: \(\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)
\(=3+\sqrt{2}-3+\sqrt{2}\)
\(=2\sqrt{2}\)
PT
2
23 tháng 8 2019
F=\(\sqrt{x^2+2019}\)
=>\(F^2=x^2+2019 =>x^2+2019\)≥2019
=> \(F^2 \)min=2019=>F min=\(\sqrt{2019}\)<=>x=0
23 tháng 8 2019
G=\(\sqrt{x^2-x+1}\)=\(\sqrt{x^2-2.\frac{1}{2}.x+\frac{1}{4}+\frac{3}{4}}\)=\(\sqrt{\left(x-\frac{1}{2}\right)^2+\frac{3}{4}}\) \(\ge\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}\)
Dấu "=" xảy ra <=> x=\(\frac{1}{2}\)
Vậy minG=\(\frac{\sqrt{3}}{2}\) <=> x\(=\frac{1}{2}\)
e: Ta có: \(E=\sqrt{19+8\sqrt{3}}-\sqrt{28-6\sqrt{3}}+\sqrt{12}\)
\(=4+\sqrt{3}-3\sqrt{3}+1+2\sqrt{3}\)
=5
còn các câu khác nữa ạ!