\(\frac{\sqrt{2+\sqrt{3}}}{\sqrt{2}}=\frac{\sqrt{2+\sqrt{3}}}{\sqrt{2}}.\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}\sqrt{2+\sqrt{3}}}{\sqrt{2}\sqrt{2}}=\frac{\sqrt{2\left(2+\sqrt{3}\right)}}{2}=\frac{\sqrt{4+2\sqrt{3}}}{2}=\frac{\sqrt{3+2\sqrt{3}+1}}{2}=\frac{\sqrt{\left(1+\sqrt{3}\right)^2}}{2}=\frac{1+\sqrt{3}}{2}\)
\(\approx1,366025404....\)
1
a. \(\frac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\frac{8}{1-\sqrt{5}}\) b.\(\frac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\frac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\) c. \(\sqrt{\frac{2-\sqrt{3}}{2+\sqrt{3}}}+\sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}\)
d. \(\frac{\sqrt{3-\sqrt{5}}.\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\) e. \(\frac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\) f. \(\frac{\left(\sqrt{5}+2\right)^2-8\sqrt{5}}{2\sqrt{5}-4}\)
Tính
a) \(\frac{10}{\sqrt{5}}+\frac{8}{3 +\sqrt{5}}-\frac{\sqrt{15}-2\sqrt{5}}{\sqrt{3}-2}\)
b) \(\left(\frac{\sqrt{14}-\sqrt{7}}{\sqrt{2}-1}-\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{5}-\sqrt{7}}\)
Bài 1: tính:
a) \(\left(\frac{1}{2}\sqrt{\frac{1}{2}}-\frac{3}{2}\sqrt{4,5}+\frac{2}{5}\sqrt{50}\right):\frac{4}{15}\sqrt{\frac{1}{8}}\)
Bài 2: Rút gọn:
A= \(\left(1+\frac{a+\sqrt{a}}{\sqrt{a}+1}\right).\left(1-\frac{a-\sqrt{a}}{\sqrt{a}-1}\right)\)Đk: (a ≥ 0, a ≠ 1)
B= \(\frac{a-3\sqrt{a}-4}{\sqrt{a}+1}\)
Bài 3: giải phương trình
a) \(\frac{\sqrt{2x-3}}{\sqrt{x-1}}=2\)
b) \(\frac{x-1}{\sqrt{x-1}}=\sqrt{x-1}\)
Bài 4: tìm giá trị nhỏ nhất:
A=\(\frac{a-\sqrt{x}+3}{\sqrt{x}+2}\) (x ≥ 0)
Rút gọn
a) ( 2 - \(\frac{a-3.\sqrt{a}}{\sqrt{a}-3}\) ) . (2 - \(\frac{5-\sqrt{a}-\sqrt{a}.b}{\sqrt{b}-5}\))
b) \(\frac{9-a}{\sqrt{a}+3}\)- \(\frac{9-6.\sqrt{a}+a}{\sqrt{a}-3}\)
Rut gon
a) ( 2- \(\frac{a-3.\sqrt{a}}{\sqrt{a}-3}\)) . ( 2- \(\frac{5.\sqrt{a}+\sqrt{a}.b}{\sqrt{b}-5}\))
b) \(\frac{9-a}{\sqrt{a}+3}\)- \(\frac{9-6.\sqrt{a}+a}{\sqrt{a}-3}\)- 6
Rut gon
a) ( 2- \(\frac{a-3.\sqrt{a}}{\sqrt{a}-3}\)) . ( 2- \(\frac{5.\sqrt{a}+\sqrt{a}.b}{\sqrt{b}-5}\))
b) \(\frac{9-a}{\sqrt{a}+3}\)- \(\frac{9-6.\sqrt{a}+a}{\sqrt{a}-3}\)- 6
\(\sqrt{\frac{5+2\sqrt{2}}{5-2\sqrt{6}}}\) + \(\sqrt{\frac{5-2\sqrt{6}}{5+2\sqrt{6}}}\)
\(\sqrt{5}\) - \(\sqrt{3-\sqrt{29-6\sqrt{20}}}\)
GIÚP MK VS MAI MK NỘP RÙI
CHỨNG MINH
a) \(\frac{\left(\sqrt{a}+1\right)^2-4\sqrt{a}}{\sqrt{a}-1}+\frac{a+\sqrt{a}}{\sqrt{a}}=2\sqrt{a}\) \(\left(a>0;a\ne1\right)\)
b) \(\frac{x\sqrt{x}+y\sqrt{y}}{\sqrt{x}+\sqrt{y}}-\left(\sqrt{x}-\sqrt{y}\right)^2=\sqrt{xy}\) \(\left(x\ge0;y\ge0\right)\)
c) \(\frac{a\sqrt{b}-b\sqrt{a}}{\sqrt{ab}}:\frac{a-b}{\sqrt{a}-\sqrt{b}}=1\) \(\left(a>0;b>0;a\ne b\right)\)
d) \(\left[\frac{\left(\sqrt{a}-\sqrt{b}\right)^2+4\sqrt{ab}}{\sqrt{a}+\sqrt{b}}-\frac{a\sqrt{b}-b\sqrt{a}}{\sqrt{ab}}\right]:\sqrt{b}=2\) \(\left(a>0;b>0\right)\)
Giúp mình với, cảm ơn mn <3
Rut gon
a)\(\frac{\left(\sqrt{x}+1\right).\left(x-\sqrt{xy}\right).\left(\sqrt{x}+\sqrt{y}\right)}{\left(x-y\right).\left(\sqrt{x^3}+x\right)}\)
b) \(\frac{\left(2-\sqrt{x}\right)^2-\left(\sqrt{x}+3\right)}{1+2.\sqrt{x}}\)
Rut gon
a)\(\frac{\left(\sqrt{x}+1\right).\left(x-\sqrt{xy}\right).\left(\sqrt{x}+\sqrt{y}\right)}{\left(x-y\right).\left(\sqrt{x^3}+x\right)}\)
b) \(\frac{\left(2-\sqrt{x}\right)^2-\left(\sqrt{x}+3\right)}{1+2.\sqrt{x}}\)
