\(=\sqrt{\left(a-2\right)+2\sqrt{a-2}+1}+\sqrt{\left(a-2\right)-2\sqrt{a-2}+1}.\)
\(=\sqrt{\left(\sqrt{a-2}+1\right)^2}+\sqrt{\left(\sqrt{a-2}-1\right)^2}.\)
\(=\sqrt{a-2}+1+\left|\sqrt{a-2}-1\right|.\)
\(M=\dfrac{\sqrt{x}+1}{\sqrt{x}-2}+\dfrac{2\sqrt{x}}{\sqrt{x}+2}+\dfrac{2+5\sqrt{x}}{4-x}\)
\(N=\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}}\right):\left(\dfrac{\sqrt{a+1}}{\sqrt{a}-2}-\dfrac{\sqrt{a}+2}{\sqrt{a}-1}\right)\)
Rút gọn :
cho P= \(\left(\dfrac{a+\sqrt{a}}{\sqrt{a}+1}+1\right)\) \(.\left(\dfrac{a-\sqrt{a}}{\sqrt{a}-1}-1\right)\) . \(\dfrac{2-\sqrt{2}}{\sqrt{2}-1}\)
a, đkxđ
b,rút tính gọn
c,tính gtbt tại a = \(\sqrt{2+\sqrt{2}}\)
chứng minh câu đẳng thức
1)\(\frac{\sqrt{a}+\sqrt{b}}{2\sqrt{a}-2\sqrt{b}}-\frac{\sqrt{a}-\sqrt{b}}{2\sqrt{a}+2\sqrt{b}}-\frac{2b}{b-a}=\frac{2\sqrt{b}}{\sqrt{a}-\sqrt{b}}\)
2)\(\left(\frac{a\sqrt{a}+b\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\right)\left(\frac{\sqrt{a}+\sqrt{b}}{a-b}\right)^2=1\)
3)\(\frac{\sqrt{a}}{\sqrt{a}-\sqrt{b}}-\frac{\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\frac{2b}{a-b}=1\)(a lớn hơn bằng 0,b lớn hơn bằng 0)
4)\(\left(1+\frac{a+\sqrt{a}}{\sqrt{a}+1}\right)\left(1-\frac{a-\sqrt{a}}{\sqrt{a}-1}\right)=1-a\)(a lớn hơn bằng 0,a khác 1)
help me:<<<
a)A=\(\dfrac{1}{2a-1}\sqrt{5a^2\left(1-4a+4a^2\right)}\) với a>\(\dfrac{1}{2}\)
b)A=\(\dfrac{\sqrt{x-2\sqrt{x-1}}}{\sqrt{x-1}-1}\)+\(\dfrac{\sqrt{x+2\sqrt{x-1}}}{\sqrt{x-1+1}}\) với x>2
c)\(\dfrac{a+b}{b^2}\)\(\sqrt{\dfrac{a^2b^4}{a^2+2ab+b^2}}\) với a+b>0; b≠0
d)A=\(\left(\sqrt{\dfrac{1-a\sqrt{a}}{1-\sqrt{a}}}+\sqrt{a}\right)\left(\dfrac{1-\sqrt{a}}{1-a}\right)^2\) với a≥0; a≠1
e)A=\(\dfrac{x-1}{\sqrt{y}-1}\sqrt{\dfrac{\left(y-2\sqrt{y}+1\right)}{\left(x-1\right)^4}}\) với x≠1; y≠1; y>o
f)A=\(\sqrt{\dfrac{m}{1-2x+x^2}}\)\(\sqrt{\dfrac{4m-8mx+4mx^2}{81}}\) với m>0; x≠4
g)A=\(\left(\dfrac{\sqrt{x}+1}{x-4}-\dfrac{\sqrt{x}-1}{x+4\sqrt{x}+4}\right)\)\(\dfrac{x\sqrt{x}+2x-4\sqrt{x}-8}{\sqrt{x}}\) với x>0; x≠4
h)\(\left(\dfrac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)\)\(\left(\dfrac{1-\sqrt{a}}{1-a}\right)^2\) với a≥0; a≠1
cho a,b,c là các số dương thoả mãn ab+bc+ac=1
Tìm GTNN\(P=\dfrac{\sqrt{a^2+1}.\sqrt{b^2+1}}{\sqrt{c^2+1}}+\dfrac{\sqrt{b^2+1}.\sqrt{c^2+1}}{\sqrt{a^2+1}}+\dfrac{\sqrt{c^2+1}.\sqrt{a^2+1}}{\sqrt{b^2+1}}\)
giải giúp mình nha!!!!!!!!!!!
bài 1: Rút gọn
C= \(\sqrt{x-2-2\sqrt{x-3}}-\sqrt{x-1-4\sqrt{x-3}}\)
D= \(\sqrt{m^2}-\sqrt{m^2-10m+25}\)
bài 2: chứng minh
a) \(\sqrt{x+2\sqrt{x-2}-1}.\left(\sqrt{x-2}-1\right):\left(\sqrt{x}-\sqrt{3}\right)=\sqrt{x}+\sqrt{3}\)
b)\(\left(\frac{1}{a-\sqrt{a}}+\frac{1}{\sqrt{a}-1}\right):\frac{\sqrt{a}+1}{a+1-2\sqrt{a}}=\frac{\sqrt{a}-1}{\sqrt{a}}\)
Chứng minh các đẳng thức sau
a.\(\left(\frac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}\frac{\sqrt{216}}{3}\right).\frac{1}{\sqrt{6}}=-1.5\)
b.\(\sqrt{\sqrt{13}-2}.\sqrt{\sqrt{13}-2}=3\)
c.\(\left(\frac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right).\left(\frac{1-\sqrt{a}}{1-a}\right)^2=1-a\) [vói a>0,a\(\ne\)1]
d.\(\left(\frac{1}{\sqrt{a}+1}-\frac{2\sqrt{a}-2}{a\sqrt{a}-\sqrt{a}+a-1}\right):\left(\frac{1}{\sqrt{a-1}}-\frac{2}{a-1}\right)=1-\frac{2}{\sqrt{a}+1}\)
Rút gọn biểu thức:
\(a,\left(\frac{\sqrt{a}+2}{a+2\sqrt{a}+1}-\frac{\sqrt{a}-2}{a-1}\right)\frac{\sqrt{a}+1}{\sqrt{a}}\)
\(b,\sqrt{\frac{a+\sqrt{a^2-b}}{2}}+\sqrt{\frac{a-\sqrt{a^2-b}}{2}}\)
P = ((sqrt(a) + 1)/(sqrt(a) - 1) - (sqrt(a) - 1)/(sqrt(a) + 1) + 4sqrt(a))(sqrt(a) - 1/(sqrt(a))) a) Rút gọn P. b) Tính giá trị của P tại a = (2 + sqrt(3))(sqrt(3) - 1) * sqrt(2 - sqrt(3))
1.\(\sqrt{2}\left(\sqrt{50}-3\sqrt{2}\right):4-\sqrt{16}\)6
2. rút gọn
\(\left(\sqrt{\frac{a}{2}}-\frac{1}{2\sqrt{a}}\right)\left(\right)\frac{a-\sqrt{a}}{\sqrt{a+1}}-\frac{a+\sqrt{a}}{\sqrt{a-1}}\left(\right)\)
