A=\(\frac{\sqrt{3}+\sqrt{11+6\sqrt{2}}-\sqrt{5+2\sqrt{6}}}{\sqrt{2}+\sqrt{6+2\sqrt{5}}-\sqrt{7+2\sqrt{10}}}=\frac{\sqrt{3}+3+\sqrt{2}-\sqrt{5+2\sqrt{6}}}{\sqrt{2}+\sqrt{5}+1-\sqrt{7+2\sqrt{10}}}\)=\(\frac{\sqrt{2}\left(\sqrt{3}+3+\sqrt{2}-\sqrt{5+2\sqrt{6}}\right)}{\sqrt{2}\left(\sqrt{2}+\sqrt{5}+1-\sqrt{7+2\sqrt{10}}\right)}\)
A=\(\frac{\sqrt{6}+3\sqrt{2}+2-\sqrt{10+4\sqrt{6}}}{2+\sqrt{10}+\sqrt{2}-\sqrt{14+4\sqrt{10}}}=\frac{\sqrt{6}+3\sqrt{2}+2-\sqrt{6}-2}{2-\sqrt{10}+\sqrt{2}-\sqrt{10}-2}=\frac{3\sqrt{2}}{\sqrt{2}}=3\)
a) \(A=\frac{\sqrt{3}+\sqrt{11+6\sqrt{2}}-\sqrt{5+2\sqrt{6}}}{\sqrt{2}+\sqrt{6+2\sqrt{5}}-\sqrt{7+2\sqrt{10}}}\)
\(A=\frac{\sqrt{3}+\sqrt{\left(\sqrt{2}+\sqrt{9}\right)^2}-\sqrt{\left(\sqrt{2}+\sqrt{3}\right)^2}}{\sqrt{2}+\sqrt{\left(1+\sqrt{5}\right)^2}-\sqrt{\left(\sqrt{2}+\sqrt{5}\right)^2}}\)
\(A=\frac{\sqrt{3}+\left|\sqrt{2}+3\right|-\left|\sqrt{2}+\sqrt{3}\right|}{\sqrt{2}+\left|1+\sqrt{5}\right|-\left|\sqrt{2}+\sqrt{5}\right|}\)
\(A=\frac{\sqrt{3}+\sqrt{2}+3-\left(\sqrt{2}+\sqrt{3}\right)}{\sqrt{2}+1+\sqrt{5}-\left(\sqrt{2}+\sqrt{5}\right)}\)
\(A=\frac{\sqrt{3}+\sqrt{2}+3-\sqrt{2}-\sqrt{3}}{\sqrt{2}+1+\sqrt{5}-\sqrt{2}-\sqrt{5}}\)
\(A=\frac{3}{1}=3\)
b) \(B=\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
\(B=\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{\left(\sqrt{3}+\sqrt{4}\right)^2}}}\)
\(B=\sqrt{5\sqrt{3}+5\sqrt{48-10.\left|\sqrt{3}+2\right|}}\)
\(B=\sqrt{5\sqrt{3}+5\sqrt{48-10.\left(\sqrt{3}+2\right)}}\)
\(B=\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{3}-20}}\)
\(B=\sqrt{5\sqrt{3}+5\sqrt{28-10\sqrt{3}}}\)
\(B=\sqrt{5\sqrt{3}+5\sqrt{\left(\sqrt{25}-\sqrt{3}\right)^2}}\)
\(B=\sqrt{5\sqrt{3}+5.\left|5-\sqrt{3}\right|}=\sqrt{5\sqrt{3}+5.\left(5-\sqrt{3}\right)}\)
\(B=\sqrt{5\sqrt{3}+25-5\sqrt{3}}=\sqrt{25}=5\)
Chúc bạn học thật giỏi nha!
