Làm:
\(F=\frac{\sqrt{a}+a\sqrt{b}-\sqrt{b}-b\sqrt{a}}{ab-1}\left(a\ge0,b\ge0,ab\ne1\right)\)
F\(=\frac{\left(\sqrt{a}-\sqrt{b}\right)+\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}{ab-1}\)
\(F=\frac{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{ab}+1\right)}{\left(\sqrt{ab}-1\right)\left(\sqrt{ab}+1\right)}=\frac{\sqrt{a}-\sqrt{b}}{\sqrt{ab}-1}\)
Kl:.....
Rút gọn:
a)\(\dfrac{\sqrt{a}+a\sqrt{b}-\sqrt{b}-b\sqrt{a}}{ab-1}\)
b) \(\dfrac{2\sqrt{15}-2\sqrt{10}+\sqrt{6}-3}{2\sqrt{5}-2\sqrt{10}-\sqrt{3}+\sqrt{6}}\)
B3: Rút gọn :
a, \(\sqrt{3}+\sqrt{8-2\sqrt{5}}\)
b, \(\sqrt{x-1-2\sqrt{x-2}}\)
Rút gọn :
a) \(\dfrac{3\sqrt{2-6}}{\sqrt{2-1}}\)
b) \(\dfrac{3\sqrt{5}+5\sqrt{3}}{\sqrt{3}+\sqrt{5}}\)
c) \(\dfrac{x-y}{\sqrt{x}-\sqrt{y}}\)
B2: rút gọn:
a, \((\sqrt{14}+\sqrt{6})(\sqrt{5}-\sqrt{21})\)
b, A= \(\sqrt{7+\sqrt{15}}-\sqrt{7-\sqrt{13}}\)
giúp em với ạ , em cảm ơn nhiều
Rút Gọn
a)\(S=\sqrt{\frac{36a^2b^6c^8}{4}}\) với a < 0; b < 0
b)\(S=\sqrt{\frac{1}{abc}\left(\sqrt{\frac{abc^2}{4}+\sqrt{\frac{ab^5c^3}{9}}}\right)}\) với a > 0 ; b > 0 ; c > 0
1. Rút gọn:
\(\sqrt{8-2\sqrt{7}}-\sqrt{9-2\sqrt{14}}\)
2. Tính:
2 + \(\sqrt{17-4\sqrt{9}+4\sqrt{5}}\)
3. CM:
a. \(\frac{x+y}{2}\) >= \(\sqrt{xy}\) với x, y >= 0
b. \(\frac{x}{y}+\frac{y}{x}\) >= 2 với x,y >= 0
c. a + b + 1 >= \(\sqrt{ab}\) + \(\sqrt{a}+\sqrt{b}\) với a,b >= 0.
Rút gọn biểu thức
A. \(\dfrac{a+b+2\sqrt{ab}}{\sqrt{a}+\sqrt{b}}-\dfrac{a-b}{\sqrt{a}+\sqrt{b}}\)
\(\dfrac{\sqrt{ }}{\sqrt{ }}\)
1. Rút gọn:
\(\sqrt{8-2\sqrt{7}}-\sqrt{9-2\sqrt{14}}\)
\(\sqrt{5-2\sqrt{6}}-\sqrt{11-4\sqrt{6}}\)
2. Tính:
a. 2 + \(\sqrt{17-4\sqrt{9}+4\sqrt{5}}\)
b. \(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7}+4\sqrt{3}}}\)
c. \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
3. CM:
a. \(\frac{x+y}{2}\) >= \(\sqrt{xy}\) với x, y >= 0
b. \(\frac{x}{y}+\frac{y}{x}\) >= 2 với x,y >= 0
c. a + b + 1 >= \(\sqrt{ab}\) + \(\sqrt{a}+\sqrt{b}\) với a,b >= 0.
Bài 1 : Rút gọn
a) \(\frac{\sqrt{6}+\sqrt{16}}{2\sqrt{3}+\sqrt{28}}\)
b) \(\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3+\sqrt{4}}}\)
Bài 2: Chứng minh
a)\(\sqrt{9-\sqrt{17}}-\sqrt{9+\sqrt{17}}=8\)
b)\(2\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}=9\)