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mi tích tau tau tích mi xong tau trả lời nka
việt nam nói là làm
a,( √6+2)(√3-√2)
<=> ( √2√3+2)(√3-√2)
<=> √2(√3+√2)(√3-√2)
<=> √2( (√3)2-(√2)2) = √2
b, (√3+1)2-2√3+4
<=> (√3)2 +2√3 +1 -2√3+4 =8
c, (1+√2-√3)(√2+√3)
<=>√2+√3+(√2)2+√6-√6-(√3)2
<=> √2+√3-1
d, √3(√2-√3)2-(√3+√2)
<=> √3( 2-2√6+3)-√3-√2
<=> 5√3-2√18-√3-√2
<=> 4√3-√2(√36-1)
<=> 4√3 - 3√2
e, (1+2√3-√2)(1+2√3+√2)
<=> (1+2√3)2-(√2)2
<=> (1+4√3+(2√3)2)-2
<=> 1+4√3+12-2= 11+4√3
g, (1-√3)2(1+2√3)2
<=>(1-2√3+3)(1+4√3+12)
<=>( 4-2√3)(13+4√3)
<=> 52+16√3-26√3-24
<=> -10√3+28
\(a,\left(1+\frac{a-\sqrt{a}}{\sqrt{a}-1}\right)\left(1-\frac{a+\sqrt{a}}{1+\sqrt{a}}\right)=\left(1+\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}\right)\left(1-\frac{\sqrt{a}\left(\sqrt{a}+1\right)}{\sqrt{a}+1}\right)\)
\(=\left(1+\sqrt{a}\right)\left(1-\sqrt{a}\right)=1^2-\sqrt{a}^2=1-a\)
\(b,\left(2-\frac{a-3\sqrt{a}}{\sqrt{a}-3}\right)\left(2-\frac{5\sqrt{a}-\sqrt{ab}}{\sqrt{b}-5}\right)=\left(2-\frac{\sqrt{a}\left(\sqrt{a}-3\right)}{\sqrt{a}-3}\right)\left(2-\frac{-\sqrt{a}\left(\sqrt{b}-5\right)}{\sqrt{b}-5}\right)\)
\(=\left(2-\sqrt{a}\right)\left(2+\sqrt{a}\right)=2^2-\sqrt{a}^2=2-a\)
\(c,\left(3+\frac{a-2\sqrt{a}}{\sqrt{a}-2}\right)\left(3-\frac{3a+\sqrt{a}}{3\sqrt{a}+1}\right)=\left(3+\frac{\sqrt{a}\left(\sqrt{a}-2\right)}{\sqrt{a}-2}\right)\left(3-\frac{\sqrt{a}\left(3\sqrt{a}+1\right)}{3\sqrt{a}+1}\right)\)
\(=\left(3+\sqrt{a}\right)\left(3-\sqrt{a}\right)=3^2-\sqrt{a}^2=3-a\)
\(d,\left(\frac{a-\sqrt{a}}{\sqrt{a}-1}+2\right)\left(2-\frac{\sqrt{a}+a}{1+\sqrt{a}}\right)=\left(\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}+2\right)\left(2-\frac{\sqrt{a}\left(\sqrt{a}+1\right)}{\sqrt{a}+1}\right)\)
\(=\left(\sqrt{a}+2\right)\left(2-\sqrt{a}\right)=2^2-\sqrt{a}^2=2-a\)
\(a.\dfrac{3\sqrt{2}-2\sqrt{3}}{\sqrt{3}-\sqrt{2}}-\dfrac{3}{3-\sqrt{6}}=\dfrac{\sqrt{6}\left(\sqrt{3}-\sqrt{2}\right)}{\sqrt{3}-\sqrt{2}}-\dfrac{\sqrt{3}.\sqrt{3}}{\sqrt{3}\left(\sqrt{3}-\sqrt{2}\right)}=\sqrt{6}-\dfrac{\sqrt{3}}{\sqrt{3}-\sqrt{2}}=\dfrac{3\sqrt{2}-3\sqrt{3}}{\sqrt{3}-\sqrt{2}}=\dfrac{-3\left(\sqrt{3}-\sqrt{2}\right)}{\sqrt{3}-\sqrt{2}}=-3\) \(b.\left(2\sqrt{2}-\sqrt{3}\right)^2-2\sqrt{3}\left(\sqrt{3}-2\sqrt{2}\right)=\left(2\sqrt{2}-\sqrt{3}\right)\left(2\sqrt{2}+\sqrt{3}\right)=8-3=5\) \(c.\left(\dfrac{1}{3-\sqrt{5}}-\dfrac{1}{3+\sqrt{5}}\right):\dfrac{5-\sqrt{5}}{\sqrt{5}-1}=\dfrac{3+\sqrt{5}-3+\sqrt{5}}{9-5}:\sqrt{5}=\dfrac{2\sqrt{5}}{4}.\dfrac{1}{\sqrt{5}}=\dfrac{\sqrt{5}}{2}.\dfrac{1}{\sqrt{5}}=\dfrac{1}{2}\) \(d.\left(3-\dfrac{a-2\sqrt{a}}{\sqrt{a}-2}\right)\left(3+\dfrac{\sqrt{ab}-3\sqrt{a}}{\sqrt{b}-3}\right)=\left(3-\sqrt{a}\right)\left(3+\sqrt{a}\right)=9-a\)
a)
\(\sqrt[3]{(\sqrt{2}+1)(3+2\sqrt{2})}=\sqrt[3]{(\sqrt{2}+1)(2+2\sqrt{2}+1)}\)
\(=\sqrt[3]{(\sqrt{2}+1)(\sqrt{2}+1)^2}=\sqrt[3]{(\sqrt{2}+1)^3}=\sqrt{2}+1\)
b)
\(\sqrt[3]{(4-2\sqrt{3})(\sqrt{3}-1)}=\sqrt[3]{(3-2\sqrt{3}+1)(\sqrt{3}-1)}\)
\(=\sqrt[3]{(\sqrt{3}-1)^2(\sqrt{3}-1)}=\sqrt[3]{(\sqrt{3}-1)^3}=\sqrt{3}-1\)
c)
\((\sqrt[3]{4}+1)^3-(\sqrt[3]{4}-1)^3=[(\sqrt[3]{4}+1-(\sqrt[3]{4}-1)][(\sqrt[3]{4}+1)^2+(\sqrt[3]{4}+1)(\sqrt[3]{4}-1)+(\sqrt[3]{4}-1)^2]\)
\(=2[\sqrt[3]{16}+1+2\sqrt[3]{4}+\sqrt[3]{16}-1+\sqrt[3]{16}+1-2\sqrt[3]{4}]\)
\(=2(3\sqrt[3]{16}+1)\)
d)
\((\sqrt[3]{9}-\sqrt[3]{6}+\sqrt[3]{4})(\sqrt[3]{3}+\sqrt[3]{2})=[(\sqrt[3]{3})^2-\sqrt[3]{3}.\sqrt[3]{2}+(\sqrt[3]{2})^2](\sqrt[3]{3}+\sqrt[3]{2})\)
\(=(\sqrt[3]{3})^3+(\sqrt[3]{2})^3=3+2=5\)
e)
\(E=\sqrt[3]{20+14\sqrt{2}}+\sqrt[3]{20-14\sqrt{2}}\)
Áp dụng công thức $(a+b)^3=a^3+b^3+3ab(a+b)$ ta có:
\(E^3=20+14\sqrt{2}+20-14\sqrt{2}+3\sqrt[3]{(20+14\sqrt{2})(20-14\sqrt{2})}.E\)
\(E^3=40+3\sqrt[3]{20^2-(14\sqrt{2})^2}.E\)
\(E^3=40+3\sqrt[3]{8}.E=40+6E\)
\(\Leftrightarrow E^2(E-4)+4E(E-4)+10(E-4)=0\)
\(\Leftrightarrow (E-4)(E^2+4E+10)=0\)
Dễ thấy $E^2+4E+10=(E+2)^2+6\neq 0$ nên $E-4=0$ hay $E=4$
a, \(\sqrt{\left(2+\sqrt{5}\right)^2}-\sqrt{\left(2-\sqrt{5}\right)^2}=\left|2+\sqrt{5}\right|-\left|2-\sqrt{5}\right|=2+\sqrt{5}-2+\sqrt{5}=2\sqrt{5}\)
b, \(\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{\left(1+\sqrt{3}\right)^2}=\left|\sqrt{3}-1\right|-\left|1+\sqrt{3}\right|=\sqrt{3}-1-1-\sqrt{3}=2\)
c, \(\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}=\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{\left(\sqrt{3}+1\right)^2}\)
\(=\left|\sqrt{3}-1\right|+\left|\sqrt{3}+1\right|=\sqrt{3}-1+\sqrt{3}+1=2\sqrt{3}\)
Có \(\sqrt{3}>\sqrt{1}\)
=> \(1-\sqrt{3}< 0\)
Có \(A=\sqrt{\left(1-\sqrt{3}\right)^2+\left(1-\sqrt{3}\right)^2}\)
\(=\sqrt{2\left(1-\sqrt{3}\right)^2}=\sqrt{2}.\sqrt{\left(1-\sqrt{3}\right)^2}=\sqrt{2}.\left(\sqrt{3}-1\right)=\sqrt{6}-\sqrt{2}\)
\(B=\sqrt{\left(1+\sqrt{3}\right)^2-\left(1-\sqrt{3}\right)^2}\)
\(=\sqrt{\left(1+\sqrt{3}-1+\sqrt{3}\right)\left(1+\sqrt{3}+1-\sqrt{3}\right)}=\sqrt{2\sqrt{3}.2}=2\sqrt{3}\)