Bài 2:

a: ĐKXĐ: x>=0

\(\sqrt{3x}-5\sqrt{12x}+7\cdot\sqrt{27x}=12\)

=>\(\sqrt{3x}-5\cdot2\sqrt{3x}+7\cdot3\sqrt{3x}=12\)

=>\(12\sqrt{3x}=12\)

=>\(\sqrt{3x}=1\)

=>3x=1

=>x=1/3(nhận)

Bài 1:

a: \(A=\left(\sqrt{\frac23}+\sqrt{\frac{50}{3}}-\sqrt{24}\right)\cdot\sqrt6\)

\(=\left(\frac{2\sqrt6}{6}+\sqrt{\frac{100}{6}}-2\sqrt6\right)\cdot\sqrt6\)

\(=2+\sqrt{100}-2\cdot6=2+10-12=0\)

b: \(B=\left(\frac{\sqrt{14}-\sqrt7}{\sqrt2-1}+\frac{\sqrt{15}-\sqrt5}{\sqrt3-1}\right):\frac{1}{\sqrt7-\sqrt5}\)

\(=\left(\frac{\sqrt7\left(\sqrt2-1\right)}{\sqrt2-1}+\frac{\sqrt5\left(\sqrt3-1\right)}{\sqrt3-1}\right)\cdot\left(\sqrt7-\sqrt5\right)\)

\(=\left(\sqrt7+\sqrt5\right)\left(\sqrt7-\sqrt5\right)\)

=7-5

=2

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`sqrt{3-sqrt5}-sqrt{3+sqrt5}`

`=sqrt{(6-2sqrt5)/2}-sqrt{(6+2sqrt5)/2}`

`=sqrt{(sqrt5-1)^2/2}-sqrt{(sqrt5+1)^2/2}`

`=(sqrt5-1)/sqrt2-(sqrt5+1)/sqrt2`

`=(sqrt5-1-sqrt5-1)/sqrt2`

`=(-2)/sqrt2=-sqrt2`

\(B=50-3\sqrt{98}+2\sqrt{8}+3\sqrt{32}-5\sqrt{18}\)

\(=50-3.\sqrt{7^2.2}+2\sqrt{2^2.2}+3\sqrt{4^2.2}-5\sqrt{3^2.2}\)

\(=50-3.7\sqrt{2}+2.2\sqrt{2}+3.4\sqrt{2}-5.3\sqrt{2}\)

\(=50-21\sqrt{2}+4\sqrt{2}+12\sqrt{2}-15\sqrt{2}\)

\(=50+\sqrt{2}.\left(-21+4+12-15\right)\)

\(=50+\sqrt{2}.\left(-20\right)\)

\(=50-20\sqrt{2}\)

\(C=\left(\sqrt{3}+\sqrt{5}+\sqrt{7}\right)\left(\sqrt{3}+\sqrt{5}-\sqrt{7}\right)\)

\(=\left(\sqrt{3}+\sqrt{5}\right)^2-\sqrt{7}^2\)

\(=\sqrt{3}^2+2.\sqrt{3}.\sqrt{5}+\sqrt{5}^2-7\)

\(=2\sqrt{15}+3+5-7\)

\(=2\sqrt{15}+1\)

\(\dfrac{1}{\sqrt{5}}-\sqrt{3}-\dfrac{1}{\sqrt{5}}+\sqrt{3}\)

= \(\dfrac{1}{\sqrt{5}}-\dfrac{1}{\sqrt{5}}-\sqrt{3}+\sqrt{3}\)

=0

\(T=\dfrac{\sqrt{27}+3}{\sqrt{3}}=\dfrac{3\sqrt{3}+3}{\sqrt{3}}=\dfrac{3\left(\sqrt{3}+1\right)}{\sqrt{3}}=\sqrt{3}\left(\sqrt{3}+1\right)=3+\sqrt{3}\)

`T=\sqrt{27}+3/\sqrt{3}`

`T=3\sqrt{3}+\sqrt{3}`

`T=4\sqrt{3}`

a)

\(7\sqrt{12}+\frac{1}{3}\sqrt{27}-\sqrt{75}\)

\(=14\sqrt{3}+\sqrt{3}-5\sqrt{3}\)

\(=10\sqrt{3}\)

b)

\(\left(2\sqrt{20}+\sqrt{125}-3\sqrt{80}\right):5\)

\(=\left(4\sqrt{5}+5\sqrt{5}-12\sqrt{5}\right):5\)

\(=-3\sqrt{5}:5\)

\(=\frac{-3\sqrt{5}}{5}\)

c)

\(3\sqrt{12a}-5\sqrt{3a}+\sqrt{48a}\)

\(=6\sqrt{3a}-5\sqrt{3a}+4\sqrt{3a}\)

\(=5\sqrt{3a}\)

\(m=\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\frac{x^2+\sqrt{x}}{x-\sqrt{x}+1}\) +x+1

\(=\frac{\sqrt{x}\left(x\sqrt{x}-1\right)}{x+\sqrt{x}+1}-\frac{\sqrt{x}\left(x\sqrt{x}+1\right)}{x-\sqrt{x}+1}+x+1\)

\(=\sqrt{x}\left(\sqrt{x}-1\right)-\sqrt{x}\left(\sqrt{x}+1\right)+x+1=x-\sqrt{x}-x-\sqrt{x}+x+1=x-2\sqrt{x}+1=\left(\sqrt{x}-1\right)^2\)