\(A=\sqrt[3]{\left(\frac{1}{2}+\frac{1}{2}\sqrt{13}\right)^3}+\sqrt[3]{\left(\frac{1}{2}-\frac{1}{2}\sqrt{13}\right)^3}\)

\(=\frac{1}{2}+\frac{\sqrt{13}}{2}+\frac{1}{2}-\frac{\sqrt{13}}{2}=1\)

\(B=\sqrt[3]{\left(2+\sqrt{2}\right)^3}+\sqrt[3]{\left(2-\sqrt{2}\right)^3}=2+\sqrt{2}+2-\sqrt{2}=4\)

1) Đk: \(x\ge4\)

\(\dfrac{\sqrt{x^2-16}}{\sqrt{x-3}}+\sqrt{x-3}=\dfrac{7}{\sqrt{x-3}}\)

\(\Leftrightarrow\dfrac{\sqrt{x^2-16}}{\sqrt{x-3}}+\dfrac{x-3}{\sqrt{x-3}}=\dfrac{7}{\sqrt{x-3}}\)

\(\Leftrightarrow\dfrac{\sqrt{x^2-16}+x-10}{\sqrt{x-3}}=0\)

\(\Leftrightarrow\sqrt{x^2-16}+x-10=0\)

\(\Leftrightarrow\sqrt{x^2-16}=10-x\)

\(\Leftrightarrow\left\{{}\begin{matrix}x^2-16=100-20x+x^2\\x\le10\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}20x=116\\x\le10\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{29}{5}\left(N\right)\\x\le10\end{matrix}\right.\)

Kl: x= 29/5

2) Đk: \(x\ge-1\)

\(x^2-5x+14=4\sqrt{x+1}\)

\(\Leftrightarrow x^4+25x^2+196-10x^3-140x+28x^2=16x+16\)

\(\Leftrightarrow x^4-10x^3+53x^2-156x+180=0\)

\(\Leftrightarrow\left(x-3\right)\left(x^3-7x^2+32x-60\right)=0\)

\(\Leftrightarrow\left(x-3\right)^2\left(x^2-4x+20\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x^2-4x+20=0\left(vn\right)\end{matrix}\right.\)

\(\Leftrightarrow x=3\left(N\right)\)

Kl: x=3

cảm ơn nhìu

Ta có: \(\left(\sqrt{14}+\sqrt{10}\right)\sqrt{6-\sqrt{35}}-2\)

\(=\sqrt{2}\cdot\left(\sqrt{7}+\sqrt{5}\right)\sqrt{6-\sqrt{35}}-2\)

\(=\left(\sqrt{7}+\sqrt{5}\right)\sqrt{12-2\sqrt{35}}-2\)

\(=\left(\sqrt{7}+\sqrt{5}\right)\sqrt{7-2\sqrt{35}+5}-2\)

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

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

\(=7-5-2\)

\(=0\)

\(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+\sqrt{48}}}}\)

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

\(=\sqrt{5\sqrt{3}+5\sqrt{48-20+10\sqrt{3}}}\)

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

\(=\sqrt{5\sqrt{3}+25-5\sqrt{3}}\)

= 5

\(\dfrac{\sqrt{3}-\sqrt{5+\sqrt{24}}+\sqrt{\sqrt{72}+11}}{\sqrt{6+\sqrt{20}}+\sqrt{2}-\sqrt{7+\sqrt{40}}}\)

\(=\dfrac{\sqrt{3}-\sqrt{\left(\sqrt{2}+\sqrt{3}\right)^2}+\sqrt{\left(3+\sqrt{2}\right)^2}}{\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{2}-\sqrt{\left(\sqrt{2}+\sqrt{5}\right)^2}}\)

\(=\dfrac{\sqrt{3}-\sqrt{2}-\sqrt{3}+3+\sqrt{2}}{\sqrt{5}+1+\sqrt{2}-\sqrt{2}-\sqrt{5}}\)

\(=3\)