\(A=\sqrt{3-\sqrt{5-2\sqrt{3}}}-\sqrt{3+\sqrt{5+2\sqrt{3}}}\)
\(A^2=\left(\sqrt{3-\sqrt{5-2\sqrt{3}}}-\sqrt{3+\sqrt{5+2\sqrt{3}}}\right)^2\)
\(A^2=\left(3-\sqrt{5-2\sqrt{3}}\right)-2\sqrt{\left(3-\sqrt{5-2\sqrt{3}}\right)\left(3+\sqrt{5+2\sqrt{3}}\right)}+\left(3+\sqrt{5+2\sqrt{3}}\right)\)
\(A^2=\left(3-\sqrt{5-2\sqrt{3}}\right)-2\sqrt{9+3\sqrt{5+2\sqrt{3}}-3\sqrt{5-2\sqrt{3}}-\sqrt{\left(5-2\sqrt{3}\right)\left(5+2\sqrt{3}\right)}}+\left(3+\sqrt{5+2\sqrt{3}}\right)\)
b3 : rút gọn
A=\(\sqrt{3+\sqrt{5+2\sqrt{3}}}.\sqrt{3-\sqrt{5+2\sqrt{3}}}\)
B= \(\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2}+\sqrt{2}}.\sqrt{2-\sqrt{2}+\sqrt{2}}\)
Rút gọn:
\(A=\dfrac{8\sqrt{41}}{\sqrt{45+4\sqrt{41}}+\sqrt{45-4\sqrt{41}}}:\left(\sqrt{3}-\sqrt{2}\right)\)
b4 : rút gọn
A=\(\sqrt{7-\sqrt{27}}+\sqrt{7+\sqrt{24}}\)
B= \(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)
Giải:
\(\left\{{}\begin{matrix}3\sqrt{x-2}+2\sqrt{y+1}=7\\5\sqrt{x-2}-3\sqrt{y+1}=-1\end{matrix}\right.\)
B1 :tìm các giá trị của x để các biểu thức sau có nghĩa
a)A=\(\dfrac{1}{1-\sqrt{x^2-3}}\)
b) B= 3\(-\sqrt{1-10x^2}\)
c) C=\(\sqrt{8x-x^2-15}\)
giúp mình với
\(C=\left(\dfrac{x+\sqrt{x}}{x\sqrt{x}+x+\sqrt{x}+1}+\dfrac{1}{1+x}\right):\dfrac{\sqrt{x}-1}{1+x}\)
a) Rút gọn C
b) x > 1. Tìm \(\sqrt{x}\cdot C\)
bài 2 : cho x,y,z >0 thỏa mãn
\(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}>\dfrac{1}{\sqrt{xy}+}\dfrac{1}{\sqrt{yz}}+\dfrac{1}{\sqrt{xz}}\)
\(\sqrt{x^2+x-5}+2\left(x+2\right)\left(x-1\right)=61\)
Rút gọn biểu thức
a, (x-2).(x+2)+(x-3).(x+3)-2x^2
b, (x+5).(x-5)+(x-7).(x+7)-2x^2
