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a) \(\left(2-\sqrt{2}\right)\left(-5\sqrt{2}\right)-\left(3\sqrt{2}-5\right)^2\)
\(=-10\sqrt{2}+5.2-\left(18-30\sqrt{2}+25\right)\)
\(=-10\sqrt{2}+10-18+30\sqrt{2}-25\)
\(=20\sqrt{2}-33\)
b) câu b đề sai
a) \(\sqrt{\left(\sqrt{7-2}\right)^2}=\sqrt{5}\)
b)\(\sqrt{\left(\sqrt{2}-1\right)^2}-\sqrt{\left(2-3\sqrt{2}\right)^2}\)
=\(\sqrt{2}-1-2+3\sqrt{2}=4\sqrt{2}-3\)
c)\(\sqrt{4+2\sqrt{3}}+\sqrt{4-2\sqrt{3}}\)
=\(\sqrt{\left(\sqrt{3}+1\right)^2}+\sqrt{\left(\sqrt{3}-1\right)^2}=2\sqrt{3}\)
d) hình như bn ghi sai
e)\(\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}}+\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}\)
=\(\left(\dfrac{\sqrt{2+\sqrt{3}}}{\sqrt{4-2\sqrt{3}}}+\dfrac{\sqrt{2-\sqrt{3}}}{\sqrt{4+2\sqrt{3}}}\right):\sqrt{2}\)
=\(\left(\dfrac{\sqrt{2+\sqrt{3}}}{\sqrt{3}-1}+\dfrac{\sqrt{2-\sqrt{3}}}{\sqrt{3}+1}\right):\sqrt{2}\)
=\(\dfrac{\sqrt{2+\sqrt{3}}\left(\sqrt{3}+1\right)+\sqrt{2-\sqrt{3}}\left(\sqrt{3}-1\right)}{2\sqrt{2}}\)
=\(\dfrac{\sqrt{6+3}+\sqrt{2+\sqrt{3}}+\sqrt{6-3}-\sqrt{2+\sqrt{3}}}{2\sqrt{2}}\)
=\(\dfrac{3+\sqrt{2+\sqrt{3}}+\sqrt{3}-\sqrt{2+\sqrt{3}}}{2\sqrt{2}}\)
=\(\dfrac{3+\sqrt{3}}{2\sqrt{2}}\)
f) \(\sqrt{9a^2}+3a-7=-3a+3a-7=-7\)
g)\(\dfrac{\sqrt{4x^2-4x+1}}{4x-2}+3x+2\)
=\(\dfrac{\sqrt{\left(2x-1\right)^2}}{4x-2}+3x+2=\dfrac{2x-1}{2\left(2x-1\right)}+3x+2\)
=\(\dfrac{1}{2}+3x+2=\dfrac{5}{2}+3x\)
h)\(\sqrt{\left(5a-1\right)^2}+2a-3\)
nếu a<0 :\(-5a+1+2a-3=-3a-2\)
nếu a>0 : \(5a-1+2a-3=7a-4\)
i)\(\sqrt{\dfrac{2a}{5}}.\sqrt{\dfrac{5a}{18}}+2\left(a-1\right)\)
=\(\sqrt{\dfrac{10a^2}{90}}+2a-2=\sqrt{\dfrac{a^2}{9}}+2a-2\)
=\(\dfrac{a}{3}+2a-2=\dfrac{7a}{3}-2\)
\(=\dfrac{a\sqrt{a}+b\sqrt{b}+3\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)-b\sqrt{b}+2a\sqrt{a}}{\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)}-\dfrac{3\sqrt{a}\left(\sqrt{a}+\sqrt{b}\right)}{a-b}\)
\(=\dfrac{3a\sqrt{a}+3\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)}{\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)}-\dfrac{3\sqrt{a}}{\sqrt{a}-\sqrt{b}}\)
\(=\dfrac{3\sqrt{a}\left(a+\sqrt{ab}+b\right)}{\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)}-\dfrac{3\sqrt{a}}{\sqrt{a}-\sqrt{b}}\)
=0
a: \(A=\left(\dfrac{a-1}{2\sqrt{a}}\right)^2\cdot\dfrac{a-2\sqrt{a}+1-a-2\sqrt{a}-1}{a-1}\)
\(=\dfrac{\left(a-1\right)^2}{4a}\cdot\dfrac{-4\sqrt{a}}{a-1}\)
\(=\dfrac{-\left(a-1\right)}{\sqrt{a}}\)
b: \(=1+\left(\dfrac{\left(2\sqrt{a}-1\right)}{1-\sqrt{a}}+\dfrac{2a\sqrt{a}-\sqrt{a}+a}{\left(\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)}\right)\cdot\dfrac{a-\sqrt{a}}{2\sqrt{a}-1}\)
Δ\(=1+\left(\dfrac{\left(-2\sqrt{a}+1\right)}{\sqrt{a}-1}+\dfrac{2a\sqrt{a}-\sqrt{a}+a}{\left(\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)}\right)\cdot\dfrac{a-\sqrt{a}}{2\sqrt{a}-1}\)
\(=1+\left(\dfrac{-2a\sqrt{a}-\sqrt{a}+1+2a\sqrt{a}-\sqrt{a}+a}{a+\sqrt{a}+1}\cdot\dfrac{\sqrt{a}}{2\sqrt{a}-1}\right)\)
\(=1+\dfrac{\left(\sqrt{a}-1\right)^2\cdot\sqrt{a}}{\left(2\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)}\)
\(=\dfrac{2a\sqrt{a}+2a+2\sqrt{a}-a-\sqrt{a}-1+a\sqrt{a}-2a+\sqrt{a}}{\left(2\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)}\)
\(=\dfrac{3a\sqrt{a}-a+2\sqrt{a}-1}{\left(2\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)}\)
a. \(\sqrt{\dfrac{3a}{2}}.\sqrt{\dfrac{2a}{75}}=\sqrt{\dfrac{3a.2a}{2.75}}=\sqrt{\dfrac{3a^2}{75}}=\sqrt{\dfrac{a^2}{25}}=\dfrac{\sqrt{a^2}}{\sqrt{25}}=\dfrac{a}{5}\)
b.\(\sqrt{5a}.\sqrt{\dfrac{2a}{a}}=\sqrt{5a}.\sqrt{2}=\sqrt{10a}\)
a.\(\sqrt{\dfrac{3a}{2}}.\sqrt{\dfrac{2a}{75}}=\dfrac{\sqrt{3a}}{\sqrt{2}}.\dfrac{\sqrt{2a}}{\sqrt{25}.\sqrt{3}}=\dfrac{a}{5}\) b. \(\sqrt{5a}.\sqrt{\dfrac{2a}{a}}=\dfrac{\sqrt{5}.\sqrt{a}.\sqrt{2a}}{\sqrt{a}}=\sqrt{10a}\)