Rut gon bieu thuc
1)\(\left(a-b\right).\sqrt{\frac{ab}{\left(a-b\right)^2}}\) voi a \(\ne\) b
2)\(\frac{x-y}{y}.\sqrt{\frac{y^4}{x^2-2xy+y^2}}\) voi x\(\ne\) y
Cho bieu thuc p=\(\left(\frac{\sqrt{a}}{2}-\frac{1}{2\sqrt{a}}\right)^2.\left(\frac{\sqrt{a}}{\sqrt{a}+1}-\frac{\sqrt{a}+1}{\sqrt{a}-1}\right)\)
a/tim dkxd va rut gon p
b/ tìm giá trị của a để p<0
Cho x=\(\sqrt{\frac{a}{b}}+\sqrt{\frac{b}{a}}\) voi a<0 ;b<0
a)CMR:\(x^2-4\ge0\)
b)Rut gon :\(\sqrt{x^2-4}\)
Cho B=\(\sqrt{\frac{\left(x-2\right)^4}{\left(3-x\right)^2}}+\frac{x^2+1}{x-3}\)
a)Rut gon B khi x<3
b)Tinh B khi x=0,5
Rut gon
\(\left(2-\frac{a-3\sqrt{a}}{\sqrt{a}-3}\right)\left(2-\frac{5\sqrt{a-\sqrt{ab}}}{\sqrt{b}-5}\right)\) voi a,b >0 a#3 ,b#25
cho \(ax^3=by^3=cz^3\)và \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1\)
CMR: \(\sqrt[3]{ax^2+by^2+cz^2}=\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}\)
Cho M=\(2x-3-\sqrt{4x^2-12x+9}\)
a) Rut gon M
b) Tinh M khi x=\(x=\frac{5}{2};x=\frac{-1}{5}\)
Cho biểu thức
A= \(\left(\frac{1}{\sqrt{a}-1}-\frac{1}{\sqrt{a}}\right):\left(\frac{\sqrt{a}+1}{\sqrt{a}-2}-\frac{\sqrt{a}+2}{\sqrt{a}-1}\right)\)
a, Rút gon A
b, Tìm a để A> \(\frac{1}{6}\)
Cho a,b,c thỏa mãn ab+bc+ca=1
C/m \(\frac{2a}{\sqrt{1+a^2}}+\frac{b}{\sqrt{1+b^2}}+\frac{c}{\sqrt{1+c^2}}\le\frac{9}{4}\)
