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19 tháng 3 2021

Trả lời:

a) Tính A khi x=9

Với x=9, A= \(\frac{\sqrt{9}}{\sqrt{9}-2}\)=3

b) Rút gọn:

T=A-B

T=\(\frac{\sqrt{x}}{\sqrt{x}-2}\)-\(\frac{2}{\sqrt{x}+2}\)-\(\frac{4\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

T=\(\frac{x-4\sqrt{x}+4}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)

T=\(\frac{\sqrt{x}-2}{\sqrt{x}+2}\)

c) Tìm x để T nguyên

T=\(\frac{\sqrt{x}-2}{\sqrt{x}+2}\)= 1-\(\frac{4}{\sqrt{x}+2}\)

T nguyên khi: 4 mod (\(\sqrt{x}\)+2)=0

=> \(\sqrt{x}+2\)={4,2,1}

=> \(\sqrt{x}\) ={2,0}

=> x={4,0}

19 tháng 3 2021

Sao bài của mình làm khi post lên olm bị mất phần sau rồi ???

18 tháng 3 2021

a, Với \(x>0;x\ne4;x\ne9\)

\(A=\left(\frac{4\sqrt{x}}{2+\sqrt{x}}+\frac{8x}{4-x}\right):\left(\frac{\sqrt{x}-1}{x-2\sqrt{x}}-\frac{2}{\sqrt{x}}\right)\)

\(=\left(\frac{4\sqrt{x}\left(2-\sqrt{x}\right)+8x}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}\right):\left(\frac{\sqrt{x}-1-2\left(\sqrt{x}-2\right)}{\sqrt{x}\left(\sqrt{x}-2\right)}\right)\)

\(=\left(\frac{8\sqrt{x}-4x+8x}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}\right):\left(\frac{\sqrt{x}-1-2\sqrt{x}+4}{\sqrt{x}\left(\sqrt{x}-2\right)}\right)\)

\(=\frac{8\sqrt{x}+4x}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}:\frac{-\sqrt{x}+3}{\sqrt{x}\left(\sqrt{x}-2\right)}\)

\(=\frac{4\sqrt{x}\left(2+\sqrt{x}\right)}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)}:\frac{3-\sqrt{x}}{\sqrt{x}\left(2-\sqrt{x}\right)}=\frac{4\sqrt{x}}{2-\sqrt{x}}.\frac{\sqrt{x}\left(2-\sqrt{x}\right)}{3-\sqrt{x}}=\frac{4x}{3-\sqrt{x}}\)

b, Ta có : A = -2 hay 

\(\frac{4x}{3-\sqrt{x}}=-2\Rightarrow4x=-6+2\sqrt{x}\)

\(\Leftrightarrow4x+6-2\sqrt{x}=0\Leftrightarrow2\left(2x+3-\sqrt{x}\right)=0\)

\(\Leftrightarrow2x+3-\sqrt{x}=0\Leftrightarrow\sqrt{x}=2x+3\)

bình phương 2 vế ta có : 

\(x=\left(2x+3\right)^2=4x^2+12x+9\)

\(\Leftrightarrow-4x^2-11x-9=0\)giải delta ta thu được : \(x=-\frac{11\pm\sqrt{23}i}{8}\)

\(a,A=\left(\frac{4\sqrt{x}}{2+\sqrt{x}}+\frac{8x}{4-x}\right):\left(\frac{\sqrt{x}-1}{x-2\sqrt{x}}-\frac{2}{\sqrt{x}}\right)\)              

\(=\left(\frac{4\sqrt{x}}{2+\sqrt{x}}+\frac{8x}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)}\right):\left(\frac{\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}-2\right)}-\frac{2}{\sqrt{x}}\right)\)

\(=\frac{4\sqrt{x}.\left(2-\sqrt{x}\right)+8x}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)}:\frac{\sqrt{x}-1-2.\left(\sqrt{x}-2\right)}{\sqrt{x}\left(\sqrt{x}-2\right)}\)

\(=\frac{8\sqrt{x}-4x+8x}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)}.\frac{\sqrt{x}\left(\sqrt{x}-2\right)}{\sqrt{x}-1-2\sqrt{x}+4}\)

\(=\frac{\left(4x+8\sqrt{x}\right)\left(\sqrt{x}\right)\left(\sqrt{x}-2\right)}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)\left(-\sqrt{x}+3\right)}\)

\(=\frac{-4\sqrt{x}\left(\sqrt{x}+2\right)\left(\sqrt{x}\right)\left(2-\sqrt{x}\right)}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)\left(-\sqrt{x}+3\right)}\)

\(=\frac{4x}{\sqrt{x}-3}\)

loading...  loading...  

a) Vì \(x=\dfrac{1}{4}\) thỏa mãn ĐKXĐ

nên Thay \(x=\dfrac{1}{4}\) vào biểu thức \(A=\dfrac{x-4}{\sqrt{x}+2}\), ta được:

\(A=\dfrac{\dfrac{1}{4}-4}{\sqrt{\dfrac{1}{4}}+2}=\left(\dfrac{1}{4}-\dfrac{16}{4}\right):\left(\dfrac{1}{2}+2\right)=\dfrac{-15}{4}:\dfrac{5}{2}\)

\(\Leftrightarrow A=\dfrac{-15}{4}\cdot\dfrac{2}{5}=\dfrac{-30}{20}=\dfrac{-3}{2}\)

Vậy: Khi \(x=\dfrac{1}{4}\) thì \(A=\dfrac{-3}{2}\)

b) Ta có: \(B=\dfrac{\sqrt{x}+1}{\sqrt{x}+2}-\dfrac{\sqrt{x}-1}{2-\sqrt{x}}-\dfrac{9-x}{4-x}\)

\(=\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}+\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\dfrac{9-x}{x-4}\)

\(=\dfrac{x-2\sqrt{x}+\sqrt{x}-2+x+2\sqrt{x}-\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\dfrac{9-x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(=\dfrac{2x-4+9-x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(=\dfrac{x+5}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

27 tháng 1 2021

Thay x = \(\dfrac{1}{4}\)vào bt A ta có: A= \(\dfrac{\dfrac{1}{4}-4}{\sqrt{\dfrac{1}{4}}+2}=\dfrac{-15}{4}:\dfrac{5}{2}=\dfrac{-3}{2}\)

Vậy x = \(\dfrac{1}{4}\)vào bt A nhận giá trị là -3/2

b)

18 tháng 10 2021

a. B = \(\dfrac{\sqrt{36}}{\sqrt{36}-3}=\dfrac{6}{6-3}=2\)

 

18 tháng 10 2021

a: Thay x=36 vào B, ta được:

\(B=\dfrac{6}{6-3}=\dfrac{6}{3}=2\)

a: Khi x=9 thì A=(9-2)/(3+2)=7/5

b: \(B=\dfrac{x-\sqrt{x}+2\sqrt{x}+2-4}{x-1}=\dfrac{x+\sqrt{x}-2}{x-1}\)

\(=\dfrac{\sqrt{x}+2}{\sqrt{x}+1}\)

c: P=A*B

\(=\dfrac{\sqrt{x}+2}{\sqrt{x}+1}\cdot\dfrac{x-2}{\sqrt{x}+2}=\dfrac{x-2}{\sqrt{x}+1}\)

P=7/4

=>(x-2)/(căn x+1)=7/4

=>4x-8=7căn 7+7

=>4x-7căn x-15=0

=>căn x=3(nhận) hoặc căn x=-5/4(loại)

=>x=9

18 tháng 11 2023

a: Khi x=25 thì \(A=\dfrac{5+1}{5-2}=\dfrac{6}{3}=2\)

b: \(B=\dfrac{\sqrt{x}}{\sqrt{x}+1}+\dfrac{1-\sqrt{x}}{\sqrt{x}-2}-\dfrac{\sqrt{x}+4}{x-\sqrt{x}-2}\)

\(=\dfrac{\sqrt{x}}{\sqrt{x}+1}+\dfrac{1-\sqrt{x}}{\sqrt{x}-2}-\dfrac{\sqrt{x}+4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}\)

\(=\dfrac{\sqrt{x}\left(\sqrt{x}-2\right)+\left(1-\sqrt{x}\right)\left(1+\sqrt{x}\right)-\sqrt{x}-4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}\)

\(=\dfrac{x-2\sqrt{x}+1-x-\sqrt{x}-4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}\)

\(=\dfrac{-3\sqrt{x}-3}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}=-\dfrac{3}{\sqrt{x}-2}\)

c: P=B:A

\(=\dfrac{-3}{\sqrt{x}-2}:\dfrac{\sqrt{x}+1}{\sqrt{x}-2}=-\dfrac{3}{\sqrt{x}+1}\)

P<-1

=>P+1<0

=>\(\dfrac{-3+\sqrt{x}+1}{\sqrt{x}+1}< 0\)

=>\(\sqrt{x}-2< 0\)

=>\(\sqrt{x}< 2\)

=>0<=x<4

mà x nguyên

nên \(x\in\left\{0;1;2;3\right\}\)

29 tháng 11 2021

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