Đặt\(a=\sqrt[3]{5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}}\Rightarrow a^3=\left(\sqrt[3]{5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}}\right)^3=5+2\sqrt{13}+5-2\sqrt{13}+3.\sqrt[3]{\left(5+2\sqrt{13}\right)\left(5-2\sqrt{13}\right)}\left(\sqrt[3]{5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}}\right)\)\(=10+3.\sqrt[3]{-27}a=10-9a\Rightarrow a^3+9a-10=0\Leftrightarrow\left(a-1\right)\left(a^2+a+10\right)=0\)
Dễ thấy \(a^2+a+10>0\forall a\inℝ\)nên a - 1 = 0 hay a = 1
Vậy \(\sqrt[3]{5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}}=1\)
Thực hiện các phép tính sau:
\(\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\)
\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
\(\sqrt{5-\sqrt{13+4\sqrt{3}}}+\sqrt{3+\sqrt{13+4\sqrt{3}}}\)
\(\sqrt{1+\sqrt{3+\sqrt{13+4\sqrt{3}}}}+\sqrt{1-\sqrt{3-\sqrt{13-4\sqrt{3}}}}\)
Tính A=\(\sqrt[3]{5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}}\)
Rút gọn các biểu thức sau:
a \(\sqrt[3]{5\sqrt{2}+7}-\sqrt[3]{5\sqrt{2}-7}\)
b \(\sqrt[3]{5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}}\)
c \(\sqrt[3]{\sqrt{5}+2}-\sqrt[3]{\sqrt{5}-2}\)
d \(\dfrac{10}{\sqrt[3]{9}-\sqrt[3]{6}+\sqrt[3]{4}}\left(\dfrac{1+\sqrt{2}}{\sqrt{4-2\sqrt{3}}}:\dfrac{\sqrt{3}+1}{\sqrt{2}-1}\right)\)
tính \(\sqrt[3]{5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}}\)
Tính : G= \(\sqrt[3]{5-2\sqrt{13}-\sqrt[3]{5-2\sqrt{13}}}\)
tính giá trị của x
a) x= \(\sqrt[3]{5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}}\)
b) x= \(\sqrt[3]{\sqrt{5}+2}-\sqrt[3]{\sqrt{5}-2}\)
c) x= \(\sqrt[3]{182+\sqrt{33125}}+\sqrt[3]{182-\sqrt{33125}}\)
Thực hiện phép tính:
A= \(\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}\)
B= \(\sqrt{13-10\sqrt{\frac{3}{2}}+}\sqrt{13+10\sqrt{\frac{3}{2}}}\)
C= \(\sqrt{5+\sqrt{3}}+\sqrt{-\sqrt{3}+5}\)
Giúp mình với
II.nhân:\(\sqrt{A}\).\(\sqrt{B}\)=\(\sqrt{..............}\)(A≥0;B≥0)
a)\(\sqrt{2}\left(\sqrt{3-\sqrt{5}}-\sqrt{3+\sqrt{5}}\right)\)
b)\(\sqrt{13+30\sqrt{2}+\sqrt{9+4\sqrt{2}}}\)
c)\(\sqrt{6+2\sqrt{5}-\sqrt{13+\sqrt{48}}}\)
Tính:
\(\sqrt{6+2\sqrt{5-\sqrt{13+4\sqrt{3}}}}\)
