\(\sqrt{4+\sqrt{8}}\cdot\sqrt{2+\sqrt{2+\sqrt{2}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2}}}\)
\(=\sqrt{4+2\sqrt{2}}\cdot\sqrt{4-2-\sqrt{2}}\)
\(=\sqrt{4+2\sqrt{2}}\cdot\sqrt{2-\sqrt{2}}\)
\(=\sqrt{8-4\sqrt{2}+4\sqrt{2}-4}=2\)
Tính \(x=\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\)
\(y=\dfrac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}\)
Giải PT:
a) -5x+7\(\sqrt{x}\) +12=0
b) \(\dfrac{1}{3}\)\(\sqrt{4x^2-20}\) +2\(\sqrt{\dfrac{x^2-5}{9}}\) -3\(\sqrt{x^2-5}=0\)
c) \(\sqrt{9x+27}+5\sqrt{x+3}-\dfrac{3}{4}\sqrt{16x+48}=5\)
d) \(\sqrt{49x-98}-14\sqrt{\dfrac{x-2}{49}}=3\sqrt{x-2}+8\)
Giải phương trình
\(a.\dfrac{3}{4}\sqrt{4x}-\sqrt{4x}+5=\dfrac{1}{4}\sqrt{4x}\)
\(b.\sqrt{3-x}-\sqrt{27-9x}+1,25.\sqrt{48-16x}=6\)
\(c.\dfrac{5\sqrt{x}-2}{8\sqrt{x}+2,5}=\dfrac{2}{7}\)
\(d.\sqrt{9x^2+12x+4}=4\)
Giải PT:
a) \(\sqrt{11+6\sqrt{2}}\) = \(\sqrt{2x^2-6x\sqrt{2}+9}\)
b) \(\sqrt{4x^2+4x\sqrt{7}+7}\) - \(\sqrt{8-2\sqrt{7}}\) = 0
c) \(\sqrt{x^2}\) = x
d) \(\sqrt{x^2-2x+1}\) = x-1
1/\(\frac{4\sqrt{2}}{2+\sqrt{2}}-\frac{4\sqrt{2}}{2-\sqrt{2}}\)
2/ \(\frac{2}{\sqrt{2}}+\sqrt{2}-2\sqrt{18}+\sqrt{\left(1-\sqrt{2}\right)^2}\)
3/ \(9\sqrt{\frac{2}{3}}+5\sqrt{54}-\sqrt{\frac{1}{2}-\frac{1}{3}}\)
4/ \(\sqrt{4+2\sqrt{2}}.\sqrt{4-2\sqrt{2}}.\left(\sqrt{8}-\sqrt{2}\right)\)
5/ \(\sqrt{14-6\sqrt{5}}+\sqrt{3-2\sqrt{2}}+\sqrt{7-2\sqrt{10}}\)
Giải các pt sau:
1) \(\sqrt{x+3}+2x\sqrt{x+1}=2x+\sqrt{x^2+4x+3}\)
2) \(2\sqrt{x+3}=9x^2-x-4\)
3) \(1+\dfrac{2}{3}\sqrt{x-x^2}=\sqrt{x}+\sqrt{1-x}\)
4) \(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=1\)
5) \(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=\dfrac{x+3}{2}\)
Tính \(\frac{2\sqrt{3}-4}{\sqrt{3}-1}+\frac{2\sqrt{2}-1}{\sqrt{2}-1}-\frac{1+\sqrt{6}}{\sqrt{2}+3}\)
\(C=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
1. \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{8}\)
2. \(\dfrac{\sqrt{3-2\sqrt{3}}}{\sqrt{17-12\sqrt{2}}}-\dfrac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)
3.\(\sqrt{7+2\sqrt{6}}-\sqrt{\left(\sqrt{6-1}\right)^2}\)
4\(\sqrt{5-2\sqrt{6}}-\sqrt{5+\sqrt{24}}\)
5.\(\sqrt{4\sqrt{5+\sqrt{3+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}}\)
6.\(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)
1. \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{8}\)
2. \(\dfrac{\sqrt{3-2\sqrt{3}}}{\sqrt{17-12\sqrt{2}}}-\dfrac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)
3.\(\sqrt{7+2\sqrt{6}}-\sqrt{\left(\sqrt{6}-1\right)^2}\)
4\(\sqrt{5-2\sqrt{6}}-\sqrt{5+\sqrt{24}}\)
5.\(\sqrt{4\sqrt{5+\sqrt{3+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}}\)
6.\(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)
