\(x=\dfrac{\left(\sqrt{5}+2\right)\sqrt[3]{\left(\sqrt{5}-2\right)^3}}{\sqrt{5}+\sqrt{14-6\sqrt{5}}}=\dfrac{\left(\sqrt{5}+2\right)\left(\sqrt{5}-2\right)}{\sqrt{5}+\sqrt{\left(3-\sqrt{5}\right)^2}}=\dfrac{5-4}{\sqrt{5}+3-\sqrt{5}}=\dfrac{1}{3}\)A=\(\left(3\left(\dfrac{1}{3}\right)^3+8\left(\dfrac{1}{3}\right)^2+2\right)^{2009}-3^{2009}=3^{2009}-3^{2009}=0\)
Cho \(x=\dfrac{\left(\sqrt{5}+2\right)\sqrt[3]{17\sqrt{5}-38}}{\sqrt{5}+\sqrt{14-6\sqrt{5}}}\)
Tính \(A=\left(3x^3+8x^2+2\right)^{1998}\)
A =\(\dfrac{x\sqrt[]{x}-3}{x-2\sqrt[]{x}-3}-\dfrac{2\left(\sqrt[]{x}-3\right)}{\sqrt[]{x}+1}+\dfrac{\sqrt[]{x}+3}{3-\sqrt[]{x}}\)
a. rút gọn A
b. Tính A với x = \(14-6\sqrt[]{5}\)
c. tìm min A
A=\(\dfrac{x\sqrt{x}-3}{x-2\sqrt{x}-3}-\dfrac{2\left(\sqrt{x}-3\right)}{\sqrt{x}+1}+\dfrac{\sqrt{x}+3}{3-\sqrt{x}}\)
a) Rút gọn A
b) Tính A với x=14-6\(\sqrt{5}\)
c) Tìm Min A
Cho x =\(\dfrac{2-\left(\sqrt{5}+2\right)\sqrt[3]{17\sqrt{5}-38}}{\sqrt{4+2\sqrt{5}}-\sqrt{3}}\)
Tính P =\(x^{11}-x^{10}+x^9-x^8+x^7-x^6+99\)
cho x = \(\sqrt[3]{38+17\sqrt{5}}+\sqrt[3]{38-17\sqrt{5}}\)
Tính C= \(\left(x^3+3x+1935\right)2018\)
1.Tính các giá trị biểu thức:
a.\(x=\sqrt[3]{5+2\sqrt{3}}+\sqrt[3]{5-2\sqrt{3}}\)
b.\(x=\sqrt[3]{\sqrt{5}+2}-\sqrt[3]{\sqrt{5}-2}\)
c.\(x=\sqrt[3]{182+\sqrt{33125}}+\sqrt[3]{182-\sqrt{33125}}\)
d.\(x=\sqrt[3]{20+14\sqrt{2}}+\sqrt[3]{20-14\sqrt{2}}\)
P=\(^{x^3+y^3}\)-3(x+y)+1969
Tính giá trị của biểu thức P với
X=\(\sqrt[3]{y}+4\sqrt{5}+\sqrt[3]{9}-4\sqrt{5}\)
Y=\(\sqrt[3]{3}+2\sqrt{2}+\sqrt{3}-2\sqrt{2}\)
a) \(\sqrt[3]{5-\sqrt{17}}+\sqrt[3]{5+\sqrt{17}}\)
b) \(\dfrac{1}{\sqrt[3]{4-\sqrt{15}}}+\sqrt[3]{4-\sqrt{15}}\)
c) \(\dfrac{\sqrt[3]{a^4}+\sqrt[3]{a^2b^2}+\sqrt[3]{b^4}}{\sqrt[3]{a^2}+\sqrt[3]{ab}+\sqrt[3]{b^2}}\)
Rút gọn các biểu thức sau
1.Chứng minh:\(\dfrac{a+\sqrt{2+\sqrt{5}.}\sqrt{\sqrt{9-4\sqrt{5}}}}{3\sqrt{2-\sqrt{5}}.\sqrt[3]{\sqrt{9+4\sqrt{5}-}3\sqrt{a^2}+\sqrt[3]{a}}}\)=\(-\sqrt[3]{a}-1\)
2.Rút gọn: \(\left(\dfrac{a^3\sqrt[]{a}-2a^3\sqrt{b}+\sqrt[3]{a^2}-\sqrt[3]{b}}{\sqrt[3]{a^2-\sqrt[3]{ab}}}+\dfrac{\sqrt[3]{a^2b}-\sqrt[3]{ab^2}}{\sqrt[3]{a}-\sqrt[3]{b}}\right)1\dfrac{1}{\sqrt[3]{a^2}}\)
