\(A=\sqrt{3+\sqrt{5}}+\sqrt{3-\sqrt{5}}\)
=>\(A^2=3+\sqrt{5}+3-\sqrt{5}+2\cdot\sqrt{9-5}\)
=>\(A^2=6+2\cdot2=10\)
=>\(A=\sqrt{10}\)
Tính
a) \(\dfrac{2}{\sqrt{3}-\sqrt{5}}+\dfrac{3-2\sqrt{3}}{\sqrt{3}-2}\)
b) \(\dfrac{5-\sqrt{5}}{\sqrt{5}-1}+\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}\)
B1. ko sử dụng máy tính, rút gọn
\(D=\dfrac{1}{2}\sqrt{48}-\dfrac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\dfrac{1}{3}}\)
\(E=\sqrt{\dfrac{3-\sqrt{5}}{3+\sqrt{5}}}-\sqrt{\dfrac{3+\sqrt{5}}{3-\sqrt{5}}}\)
\(F=\sqrt{3+\sqrt{5}}+\sqrt{7-3\sqrt{5}}-\sqrt{2}\)
B2.
\(G=\dfrac{\sqrt{x}}{x-\sqrt{x}+1}\)
so sánh G với 1
B3. giải pt
\(\left\{{}\begin{matrix}\left(x-3\right)\left(2y+5\right)=\left(2x+7\right)\left(y-1\right)\\\left(4x+1\right)\left(3y-6\right)=\left(6x-1\right)\left(2y+3\right)\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\left(x+y\right)\left(x-1\right)=\left(x-y\right)\left(x+1\right)+2xy\\\left(y-x\right)\left(y+1\right)=\left(y+x\right)\left(y-2\right)-2xy\end{matrix}\right.\)
Tính:
a/ \(\frac{3+\sqrt{5}}{\sqrt{2}+\sqrt{3+\sqrt{5}}}+\frac{3-\sqrt{5}}{\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
b/ \(\frac{\sqrt{20+8\sqrt{3}}+\sqrt{20-8\sqrt{3}}}{\sqrt{5+2\sqrt{3}}-\sqrt{5-2\sqrt{3}}}-\frac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\$\sqrt{4+\sqrt{3}}-\sqrt{4-\sqrt{3}}}\)
\(\left(3-\sqrt{5}\right)\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right)\sqrt{3-\sqrt{5}}\)
tính
\(\frac{\sqrt{5+\sqrt{3}}+\sqrt{5-\sqrt{3}}}{\sqrt{5+\sqrt{22}}}-\frac{\sqrt{6-\sqrt{24}}}{\sqrt{3+\sqrt{3}}-\sqrt{3-\sqrt{3}}}\)
Tính
Tính
\(Q=\left(3-\sqrt{5}\right)\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right)\sqrt{3-\sqrt{5}}\)
Tính : \(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}+1}{\sqrt{5}-1}\)
Tính:
1) \(\dfrac{1}{1+\sqrt{5}}+\dfrac{1}{\sqrt{5}-1}\)
2) \(\dfrac{1}{\sqrt{5}+\sqrt{3}}-\dfrac{1}{\sqrt{5}-\sqrt{3}}\)
3) \(\dfrac{1}{\sqrt{2}-\sqrt{3}}-\dfrac{1}{\sqrt{3}+\sqrt{2}}\)
4) \(\dfrac{1}{3+\sqrt{5}}+\dfrac{1}{\sqrt{5}-3}\)
5) \(\dfrac{1}{\sqrt{2}-\sqrt{6}}-\dfrac{1}{\sqrt{6}+\sqrt{2}}\)
LM CHI TIẾT GIÚP MK NHÉ
Tính :\(\sqrt{3+\sqrt{5+2\sqrt{3}}}+\sqrt{3-\sqrt{5+2\sqrt{3}}}\)
\(\frac{\sqrt{5+\sqrt{3}}+\sqrt{5-\sqrt{3}}}{\sqrt{5+\sqrt{22}}}-\frac{\sqrt{6-\sqrt{24}}}{\sqrt{3+\sqrt{3}}-\sqrt{3-\sqrt{3}}}\)
tính
