Cho a,b,c \(\ne\) 0 và a=b+c

CMR:\(P=\sqrt{\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}}\) là một số hữu tỉ

Cho \(x=\sqrt{\dfrac{2-\sqrt{3}}{2}}\) tính giá trị bt:

\(P=\left(2x^5+2x^4-x^3-1\right)^{2016}+\dfrac{\left(2x^3+2x^2-x-3\right)^{2017}}{2x^4+2x^3-x^2-3}\)

Cho: \(x=\dfrac{4\sqrt{4-\sqrt{5+\sqrt{21+\sqrt{80}}}}}{\sqrt{10}-\sqrt{2}}\)

Tính\(P=\left(x^3-4x+1\right)^{2018}\)

cho \(a=\dfrac{\sqrt{6}+\sqrt{2}}{2};b=\dfrac{\sqrt{6}-\sqrt{2}}{2}\)

tính giá trị bt: \(B=\dfrac{1}{a^7}+\dfrac{1}{b^7}\)

cho \(x=\dfrac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)

\(y=\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\)

tính giá trị bt: \(A=\dfrac{xy-1}{x+y}-\dfrac{1-xy}{2x-y}\)

rút gọn:

\(C=\sqrt{\dfrac{1}{1^2}+\dfrac{1}{2^2}+\dfrac{1}{3^2}}+\sqrt{\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}}+...+\sqrt{\dfrac{1}{1^2}+\dfrac{1}{1999^2}+\dfrac{1}{2000^2}}\)

rút gọn:

\(B=\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}-\sqrt{5}\)

rút gọn:

\(A=\dfrac{3+\sqrt{5}}{\sqrt{10}+\sqrt{3+\sqrt{5}}}-\dfrac{3-\sqrt{5}}{\sqrt{10}-\sqrt{3+\sqrt{5}}}\)

cho \(x=\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2-\sqrt{2}}}\)

\(y=\dfrac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}\)

Tính giá trị biểu thức:\(Q=\dfrac{xy+1}{x+y}+\dfrac{1-xy}{x-y}\)