ab = a : b

a+m/b+m = (a + m) : (b + m)

a+m/b+m >a /b

\(A=\left(-\infty;+\infty\right);B=(1;7]\)

\(A\cap B=(1;7]\)

\(A\cup B=\left(-\infty;+\infty\right)\)

\(A\backslash B=(-\infty;1]\cup\left(7;+\infty\right)\)

\(B\text{A}=\varnothing\)

a)\(6\sqrt[3]{81}-4\sqrt[3]{375}+3\sqrt[3]{24}\)

\(=6\sqrt[3]{3^4}-4\sqrt[3]{3.5^3}+3\sqrt[3]{3.2^3}\)

\(=6.3\sqrt[3]{3}-4.5\sqrt[3]{3}+3.2\sqrt[3]{3}=4\sqrt[3]{3}\)

b)\(\sqrt[3]{3}.\sqrt[3]{144}-\dfrac{\sqrt[3]{384}}{\sqrt[3]{3}}+2\sqrt[3]{-128}\)

\(=\sqrt[3]{432}-\sqrt[3]{\dfrac{384}{3}}+2\sqrt[3]{-2.4^3}\)

\(=\sqrt[3]{6^3.2}-\sqrt[3]{2.4^3}+2.\sqrt[3]{-2.4^3}\)

\(=6\sqrt[3]{2}-4\sqrt[3]{2}+2.-4\sqrt[3]{2}==-6\sqrt[3]{2}\)

a) Ta có: \(\sqrt{3+\sqrt{5}}+\sqrt{3-\sqrt{5}}\)

\(=\dfrac{\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{5}+1+\sqrt{5}-1}{\sqrt{2}}=\dfrac{2\sqrt{5}}{\sqrt{2}}=\sqrt{10}\)

b) Ta có: \(2\sqrt{2}\left(\sqrt{3}-2\right)+\left(9+4\sqrt{2}\right)\)

\(=2\sqrt{6}-4\sqrt{2}+9+4\sqrt{2}\)

\(=9+2\sqrt{6}\)

c) Ta có: \(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\left(2+\sqrt{3}\right)}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{28-10\sqrt{3}}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\left(5-\sqrt{3}\right)}}\)

\(=\sqrt{4+\sqrt{25}}=\sqrt{4+5}=3\)(đpcm)

a) \(\sqrt[3]{3x-2}=4\Rightarrow3x-2=64\Rightarrow3x=66\Rightarrow x=22\)

b) \(\sqrt[3]{x^3+7x^2}=x+4\Rightarrow x^3+7x^2=\left(x+4\right)^3\)

\(\Rightarrow x^3+7x^2=x^3+12x^2+48x+64\Rightarrow5x^2+48x+64=0\)

\(\Rightarrow\left(x+8\right)\left(5x+8\right)=0\Rightarrow\left[{}\begin{matrix}x=-8\\x=-\dfrac{8}{5}\end{matrix}\right.\)

a) Ta có: \(\sqrt[3]{3x-2}=4\)

\(\Leftrightarrow3x-2=64\)

\(\Leftrightarrow3x=66\)

hay x=22

b) Ta có: \(\sqrt[3]{x^3+7x^2}=x+4\)

\(\Leftrightarrow x^3+7x^2=\left(x+4\right)^3\)

\(\Leftrightarrow x^3+7x^2-x^3-12x^2-48x-64=0\)

\(\Leftrightarrow-5x^2-48x-64=0\)

\(\Leftrightarrow5x^2+48x+64=0\)

\(\text{Δ}=48^2-4\cdot5\cdot64=1024\)

Vì Δ>0 nên phương trình có hai nghiệm phân biệt là:

\(\left\{{}\begin{matrix}x_1=\dfrac{-48-32}{10}=\dfrac{-80}{10}=-8\\x_2=\dfrac{-48+32}{10}=\dfrac{-16}{10}=\dfrac{-8}{5}\end{matrix}\right.\)

\(\left[a,b\right]+\left(a,b\right)=23\\ a,b=23:2\\ a,b=11,5\\ \Rightarrow a=11\\ b=5\)