\(\sqrt[3]{26-15\sqrt[]{3}}=\sqrt[3]{8-3.4.\sqrt[]{3}+3.2.3-3\sqrt[]{3}}\)
\(=\sqrt[3]{2^3-3.2^2.\sqrt[]{3}+3.2.\left(\sqrt[]{3}\right)^2-\left(\sqrt[]{3}\right)^3}\)
\(=\sqrt[3]{\left(2-\sqrt[]{3}\right)^3}=2-\sqrt[]{3}\)
\(\Rightarrow\left\{{}\begin{matrix}a=2\\b=-1\end{matrix}\right.\) \(\Rightarrow a^2-b^2=3\)
Tính GTBT:
a, \(A=^3\sqrt{20+14\sqrt{2}}+^3\sqrt{20-14\sqrt{2}}\)
\(b,B=^3\sqrt{26+15\sqrt{3}}-^3\sqrt{26-15\sqrt{3}}\)
Tính giá trị của biểu thức sau:
\(a,^3\sqrt{26+15\sqrt{3}}-^3\sqrt{26-15\sqrt{3}}\)
\(b,^3\sqrt{9+4\sqrt{5}}+^3\sqrt{9-4\sqrt{5}}\)
\(c,^3\sqrt{20+14\sqrt{2}}+^3\sqrt{20-14\sqrt{2}}\)
Tính giá trị của biểu thức sau:
\(a,^3\sqrt{26+15\sqrt{3}}-^3\sqrt{26-15\sqrt{3}}\)
\(b,^3\sqrt{9+4\sqrt{5}}+^3\sqrt{9-4\sqrt{5}}\)
\(c,^3\sqrt{20+14\sqrt{2}}+^3\sqrt{20-14\sqrt{2}}\)
\(B=\left(2-\sqrt{3}\right).\sqrt{26+15\sqrt{3}}-\left(2+\sqrt{3}\right).\sqrt{26-15\sqrt{3}}\)
\(C=\left(\sqrt{10}-\sqrt{2}\right).\sqrt{3+\sqrt{5}}\)
Tính \(S=\sqrt[3]{26+15\sqrt{3}}\left(2-\sqrt{3}\right)+\sqrt[3]{9+\sqrt{80}}+\sqrt[3]{9-\sqrt{80}}\)
1.Tính: \(\sqrt[3]{26+15\sqrt{3}}\) - \(\sqrt[3]{26-15\sqrt{3}}\)
2.Rút gọn: P=\(\left(\frac{\sqrt{a-2}+2}{3}\right)\).\(\left(\frac{\sqrt{a-2}}{3+\sqrt{a-2}}+\frac{a+7}{11-a}\right)\):\(\left(\frac{3\sqrt{a-2}+1}{a-3\sqrt{a-2}-2}-\frac{1}{\sqrt{a-2}}\right)\)
Rút gọn
A=(\(\left(2-\sqrt{3}\right).\sqrt{26+15\sqrt{3}}-\left(2+\sqrt{3}\right).\sqrt{26-15\sqrt{3}}\)
Rút gọn: (2 - \(\sqrt{3}\) )\(\sqrt{26+15\sqrt{3}}\) - (2 + \(\sqrt{3}\) )\(\sqrt{26-15\sqrt{3}}\)
\(\left(2-\sqrt{3}\right)\sqrt{26+15\sqrt{3}-\left(2+\sqrt{3}\right)\sqrt{26-15\sqrt{3}}}\)
Rút gọn: \(\sqrt[3]{15\sqrt{3}-26}-\sqrt[3]{15\sqrt{3}+26}\)
Giải chi tiết giúp em với
