Rút gọn: A = \(\sqrt{2x+\sqrt{4x+1}}+\sqrt{2x-\sqrt{4x-1}}\)\(\left(\frac{1}{4}
Rút gọn :
a) \(\sqrt{2x-\sqrt{4x-1}}-\sqrt{2x+\sqrt{4x-1}}\) (với \(\frac{1}{4}\le x\le\frac{1}{2}\)
b)\(\frac{\sqrt{x+\sqrt{4\left(x-1\right)}}-\sqrt{x-\sqrt{4\left(x-1\right)}}}{\sqrt{x^2-4\left(x-1\right)}}.\left(\sqrt{x-1}-\frac{1}{\sqrt{x-1}}\right)\)
\(P=\left(\frac{\sqrt{x}-4x}{1-4x}-1\right):\left(\frac{1+2x}{1-4x}+\frac{2\sqrt{x}}{2\sqrt{x}-1}-1\right)\)
Rút gọn P
P = \(\left(\frac{\sqrt{x}-4x}{1-4x}-1\right):\left(\frac{1+2x}{1-4x}+\frac{2\sqrt{x}}{2\sqrt{x}-1}-1\right)\)
P = \(\frac{\sqrt{x}-4x-1+4x}{1-4x}:\left(\frac{1+2x-2\sqrt{x}\left(2\sqrt{x}+1\right)-1+4x}{1-4x}\right)\)
P = \(\frac{\sqrt{x}-1}{1-4x}\cdot\frac{1-4x}{1+2x-4x-2\sqrt{x}-1+4x}\)
P = \(\frac{\sqrt{x}-1}{2x-2\sqrt{x}}\)
P = \(\frac{\sqrt{x}-1}{2\sqrt{x}\left(\sqrt{x}-1\right)}=\frac{1}{2\sqrt{x}}\)
Bài 1 : Cho biểu thức : A = 2x + \(\frac{\sqrt{9x^2-6x+1}}{1-3x}\)
a. Rút gọn A
b.Tính giá trị A khi x = -3
Bài 2 : Rút gọn :
a. \(\sqrt{a+2\sqrt{a-1}}+\sqrt{a-2\sqrt{a-1}}\)(với a \(\ge\)1)
b. \(\sqrt{2x+\sqrt{4x-1}}+\sqrt{2x-\sqrt{4x-1}}\)(với \(\frac{1}{4}< x< \frac{1}{2}\))
Bài 3 : Giải PT:
\(\sqrt{2x+\sqrt{4x-1}}+\sqrt{2x-\sqrt{4x-1}}\)= \(\sqrt{6}\)
Rút gọn A=\(\frac{\sqrt{x-\sqrt{4x-4}}+\sqrt{x+4\sqrt{4x-4}}}{\sqrt{x^2-4\left(x-1\right)}}.\left(1-\frac{1}{x-1}\right)\)
Rút gọn:
\(A=\dfrac{2}{x-1}\sqrt{\dfrac{x^2-2x+1}{4x^2}}\)
\(B=\left(x^2-4\right)\sqrt{\dfrac{9}{x^2-4x+4}}\)
\(A=\dfrac{2}{x-1}\sqrt{\dfrac{\left(x-1\right)^2}{4x^2}}=\dfrac{2}{x-1}\left|\dfrac{x-1}{2x}\right|=\dfrac{\left|x-1\right|}{\left(x-1\right)\left|x\right|}\)
\(B=\left(x^2-4\right)\sqrt{\dfrac{9}{x^2-4x+4}}=\dfrac{3\left(x^2-4\right)}{\left|x-2\right|}\)
a) Ta có: \(A=\dfrac{2}{x-1}\cdot\sqrt{\dfrac{x^2-2x+1}{4x^2}}\)
\(=\dfrac{2}{x-1}\cdot\dfrac{x-1}{2x}\)
\(=\dfrac{1}{x}\)
b) Ta có: \(\left(x^2-4\right)\cdot\sqrt{\dfrac{9}{x^2-4x+4}}\)
\(=\dfrac{\left(x-2\right)\left(x+2\right)\cdot3}{\left(x-2\right)^2}\)
\(=\dfrac{3x+6}{x-2}\)
bài 1: cho biểu thức sau:P =\(\frac{\sqrt{a}}{\sqrt{a}+3}+\frac{2\sqrt{a}}{\sqrt{a}-3}-\frac{3a+9}{a-9}\)( a>=9, a khác 9)
a, rút gọn P
b, tìm a để P = \(\frac{1}{3}\)
c, tìm max P
bài 2: rút gọn
A=\(\sqrt{2x+\sqrt{4x-1}}+\sqrt{2x-\sqrt{4x-1}}\)
B=\(53+20\sqrt{4+\sqrt{9-4\sqrt{2}}}\)
giải giúp mình bài này ới ạ mình đng cần gấp
Cho biểu thức
c=(căng x-2/căng x+2+căng x+2/căng x-2)nhân căng x+2/2 - 4 căng x/căng x-2
a)
\(P=\frac{\sqrt{a}}{\sqrt{a}+3}+\frac{2\sqrt{a}}{\sqrt{a}-3}-\frac{3a+9}{a-9}\)
\(P=\frac{\sqrt{a}}{\sqrt{a}+3}+\frac{2\sqrt{a}}{\sqrt{a}-3}-\frac{3a+9}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-3\right)}\)
\(P=\frac{\sqrt{a}\left(\sqrt{a}-3\right)}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-3\right)}+\frac{\sqrt{a}\left(\sqrt{a}+3\right)}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-3\right)}-\frac{3a+9}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-3\right)}\)
\(P=\frac{a-3\sqrt{a}+3+3\sqrt{a}-3a-9}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-3\right)}\)
\(P=\frac{-2a-3}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-3\right)}\)
\(P=\frac{-2a-3}{a-9}\)
b) Để \(P=\frac{1}{3}\Rightarrow\frac{-2a-3}{a-9}=\frac{1}{3}\)
\(\Rightarrow3\left(-2a-3\right)=a-9\)
\(\Rightarrow-6a-9=a-9\)
\(\Rightarrow-6a-a=-9+9\)
\(\Rightarrow-7a=0\left(L\right)\)
Vậy ko có gt của a để P=1/3 ( mk ko chắc.....)
A=\(\left(\frac{\sqrt{x}-4x}{1-4x}-1\right):\left(\frac{1+2x}{1-4x}-\frac{2\sqrt{x}}{2\sqrt{x}-1}-1\right)\)
a) rút gọn A
b) tìm x để \(A>A^2\)
c) tìm x để trị tuyệt đối A > \(\frac{1}{4}\)
1. Cho biểu thức:
B= ( \(\frac{\sqrt{x}}{\sqrt{x}-1}+\frac{2}{x-\sqrt{x}}\)) :\(\frac{1}{\sqrt{x}-1}\)
a) Rút gọn B
b) Tìm Min B
2. Rút gọn biểu thức:
\(\sqrt{\frac{1}{1-2x+x^2}}.\sqrt{\frac{4-4x+4x^2}{81}}\)
3. giải phương trình: 3+\(\sqrt{2x-3}\)= x
rút gọn A=\(\sqrt{2x+\sqrt{4x-1}}+\sqrt{2x-\sqrt{4x-1}}\)
B=\(53+20\sqrt{4+\sqrt{9-4\sqrt{2}}}\)