Giúp tôi giải toán và làm văn

đặt căn 2x^2-4x+6=a
căn 3x^2-6x+4=b ta được
a+b=a^2-b^2
(a+b)(a-b-1)=0
tới đây bạn giải 2 TH là được nha
k cho mình với ạ!thank bạn

\(P=\frac{4}{3}\Rightarrow\frac{\sqrt{x}+2}{\sqrt{x}+1}=\frac{4}{3}\)

\(\Leftrightarrow3\left(\sqrt{x}+2\right)=4\left(\sqrt{x}+1\right)\)

\(\Leftrightarrow3\sqrt{x}+6=4\sqrt{x}+4\)

\(\Leftrightarrow6-4=4\sqrt{x}-3\sqrt{x}\)

\(\Leftrightarrow\sqrt{x}=2\Leftrightarrow x=4\)(ko thỏa mãn ĐKXĐ)

=>pt vo nghiệm

d,\(\left(\sqrt{x}+1\right)P-\sqrt{x}-4\sqrt{x-1}+26=-6x+10\sqrt{5x}\)

\(\Leftrightarrow\left(\sqrt{x}+1\right)\frac{\sqrt{x}+2}{\sqrt{x}+1}-\sqrt{x}-4\sqrt{x-1}+26=-6x+10\sqrt{5x}\)

\(\Leftrightarrow\sqrt{x}+2-\sqrt{x}-4\sqrt{x-1}+26=-6x+10\sqrt{5x}\)

\(\Leftrightarrow-4\sqrt{x-1}+28=-6x+10\sqrt{5x}\)

\(\Leftrightarrow x=5\)

\(a,x=7-4\sqrt{3}=4-2.2\sqrt{3}+3\) (Thỏa mãn ĐKXĐ)

\(=\left(2-\sqrt{3}\right)^2\)

\(B=\frac{2}{\sqrt{x}-2}=\frac{2}{\sqrt{\left(2-\sqrt{3}\right)^2}-2}\)

\(=\frac{2}{2-\sqrt{3}-2}=-\frac{2\sqrt{3}}{3}\)

\(b,P=\frac{B}{A}=\frac{2}{\sqrt{x}-2}:\left(\frac{\sqrt{x}}{x-4}+\frac{1}{\sqrt{x}-2}\right)\)

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

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

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

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

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

\(Q=\frac{2P\sqrt{x}}{3}=\frac{2\left(\frac{3}{\sqrt{x}+3}\right)\sqrt{x}}{3}=\frac{6\sqrt{x}}{\sqrt{x}+3}\cdot\frac{1}{3}\)

\(=\frac{2\sqrt{x}}{\sqrt{x}+3}=\frac{2\sqrt{x}+6-6}{\sqrt{x}+3}=\frac{2\left(\sqrt{x}+3\right)}{\sqrt{x}+3}-\frac{6}{\sqrt{x}+3}\)

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

\(ĐểQ\in Z\Rightarrow\frac{6}{\sqrt{x}+3}\in Z\)

\(\Rightarrow\sqrt{x}+3\inƯ\left(6\right)=\left\{1;2;3;6;-1;-2;-3;-6\right\}\)

\(\Rightarrow\sqrt{x}\in\left\{-2;-1;0;3\right\}\)

\(\Rightarrow x\in\left\{0;9\right\}\)

Kết hợp ĐKXĐ \(\Rightarrow x=0\)

\(b,x=20-6\sqrt{11}=11-2.3\sqrt{11}+9\)

\(=\left(\sqrt{11}-3\right)^2\)

\(P=\frac{3}{\sqrt{x}+3}=\frac{3}{\sqrt{\left(\sqrt{11}-3\right)^2}+3}=\frac{3}{\sqrt{11}-3+3}=\frac{3\sqrt{11}}{11}\)

\(c,P>\frac{1}{2}\Rightarrow\frac{3}{\sqrt{x}+3}>\frac{1}{2}\)

\(\Leftrightarrow\frac{3}{\sqrt{x}+3}-\frac{1}{2}>0\)

\(\Leftrightarrow\frac{6-\sqrt{x}-3}{2\left(\sqrt{x}+3\right)}>0\)

\(\Leftrightarrow\frac{6-\sqrt{x}-3}{2\left(\sqrt{x}+3\right)}>0\)\(\Leftrightarrow\frac{3-\sqrt{x}}{2\left(\sqrt{x}+3\right)}>0\)

vì \(2\left(\sqrt{x}+3\right)>0\) (nếu x=0 =>pt vô nghiệm)

\(\Rightarrow3-\sqrt{x}>0\Rightarrow\sqrt{x}< 3\Rightarrow x< 9\)

Kết hợp ĐKXĐ: \(0< x< 9\)

\(P=\left(\frac{3x+3}{x-9}-\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{3-\sqrt{x}}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right).ĐKXĐ:x\ge0,x\ne9\)

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

\(=\left(\frac{3x+3-2x+6\sqrt{x}-x-3\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\right):\left(\frac{2\sqrt{x}-2-\sqrt{x}+3}{\sqrt{x}-3}\right)\)

\(=\frac{3\sqrt{x}+3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}:\frac{\sqrt{x}+1}{\sqrt{x}-3}\)

\(=\frac{3\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}.\frac{\sqrt{x}-3}{\sqrt{x}+1}\)

\(=\frac{3}{\sqrt{x}+3}\)

điều kiện x khác 0

\(\frac{5}{x^2}+\frac{2}{\sqrt{1+\frac{5}{x^2}}}=1\)

đặt \(\frac{5}{x^2}=a\left(a>0\right)\)=> a+\(\frac{2}{\sqrt{1+a}}=1\)   (1)

<=> \(1-a=\frac{2}{\sqrt{1+a}}>0=>a< 1\)

với a<1 thì \(\frac{2}{\sqrt{1+a}}>\frac{2}{\sqrt{1+1}}=\sqrt{2}>1\) kết hợp với a> 0 => (1) vô nghiệm hay pt đã cho vô nghiệm

em nhổ tóc đầu cho bạn học 13 tuổi không may bị bay mất một khoảng tóc liệu có mọc lại không xin được tư vấn

em nhổ tóc đầu cho bạn học 13 tuổi không may bị bay mất một khoảng tóc liệu có mọc lại không xin được tư vấn

ĐK: x\(\ge0\). 

Đặt \(A=\frac{\sqrt{x}}{x+\sqrt{x}+1}\)

Đặt \(t=\sqrt{x}\)( t >=0)

Có: \(A=\frac{t}{t^2+t+1}\)

<=> \(At^2+\left(A-1\right)t+A=0\)(1)

TH1: A =0 => t =0

TH2: A khác 0.

(1) có nghiệm <=> \(\Delta\ge0\Leftrightarrow\left(A-1\right)^2-4A^2\ge0\Leftrightarrow-3A^2-2A+1\ge0\Leftrightarrow-1\le A\le\frac{1}{3}\)

Do đó: A min = -1 thay vào tìm x

           A max = 1/3 thay vào tìm x .

Kết luận....

\(y=x-4\sqrt{x}-1\)

\(y=\left(\sqrt{x}\right)^2-2.\sqrt{x}.2+4-5\)

\(y=\left(\sqrt{x}-2\right)^2-5>5\)HOẶC=5

\(=>y_{min_{ }}=5< =>\sqrt{x}=2=>x=4\)

\(y=x-4\sqrt{x}-1.\)

\(y=x-2\cdot2\sqrt{x}+2-2-1\)

\(y=\left(\sqrt{x}-2\right)^2-2-1\)

\(y=\left(\sqrt{x}-2\right)^2-3\)

có \(\left(\sqrt{x}-2\right)^2\ge0\)

\(\Rightarrow\left(\sqrt{x}-2\right)^2-3\ge-3\)

\(\Rightarrow GTNNy=-3\)

với \(\left(\sqrt{x}-2\right)^2=0;x=4\)

Mik nhầm -5 chứ ko phải 5

2- căn 3

Chứng minh \(\frac{1}{\left(n+1\right)\sqrt{n}+n\sqrt{n+1}}=\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n+1}}\) rồi áp dụng với n = 1,2,....,2014

ki+e

n ejmfjnhcy

Đặt A=\(\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}\)

=>A=\(\frac{\sqrt{2}.\left(\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}\right)}{\sqrt{2}}\)

=>A=\(\frac{\sqrt{4-2\sqrt{3}}-\sqrt{4+2\sqrt{3}}}{\sqrt{2}}\)

=>A=\(\frac{\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{\left(\sqrt{3}+1\right)^2}}{\sqrt{2}}\)

=>A=\(\frac{\sqrt{3}-1+\sqrt{3}+1}{\sqrt{2}}\)(vì \(\sqrt{3}>1\)nên mih bỏ luôn trị tuyệt đối nhá)

=>A=\(\frac{2\sqrt{3}}{\sqrt{2}}=\sqrt{6}\)

Vậy A=\(\sqrt{6}\)

Chắc đúng á  =))

\(\frac{A}{\sqrt{2}}=\frac{2+\sqrt{3}}{2+\sqrt{4+2\sqrt{3}}}+\frac{2-\sqrt{3}}{2-\sqrt{4-2\sqrt{3}}}\)

 =\(\frac{2+\sqrt{3}}{3+\sqrt{3}}+\frac{2-\sqrt{3}}{3-\sqrt{3}}\) =\(\frac{\left(2+\sqrt{3}\right)\left(3-\sqrt{3}\right)+\left(2-\sqrt{3}\right)\left(3+\sqrt{3}\right)}{\left(3+\sqrt{3}\right)\left(3-\sqrt{3}\right)}\) =\(\frac{6}{6}=1\)

\(\Rightarrow A=\sqrt{2}\)

1) Ta có: \(2020^2=\left(2019+1\right)^2=2019^2+2.2019+1.\)

\(\Rightarrow1+2019^2=2020^2-2.2019\)

\(\Rightarrow M=\sqrt{1+2019^2+\frac{2019^2}{2020^2}}+\frac{2019}{2020}=\sqrt{2020^2-2.2019+\frac{2019^2}{2020^2}}+\frac{2019}{2020}\)

\(=\sqrt{2020^2-2.2020.\frac{2019}{2020}+\left(\frac{2019}{2020}\right)^2}+\frac{2019}{2020}\)

\(=\sqrt{\left(2020-\frac{2019}{2020}\right)^2}+\frac{2019}{2020}=2020-\frac{2019}{2020}+\frac{2019}{2020}\)

\(=2020\)

Vậy M=2020.

2) Xét  : \(k\in N;k\ge2\)ta có:

\(\left(1+\frac{1}{k-1}-\frac{1}{k}\right)^2=1+\frac{1}{\left(k-1\right)^2}+\frac{1}{k^2}+\frac{2}{k-1}-\frac{2}{\left(k-1\right)k}-\frac{2}{k}\)

                                          \(=1+\frac{1}{\left(k-1\right)^2}+\frac{1}{k^2}+\frac{2}{k-1}-\frac{2}{k-1}+\frac{2}{k}-\frac{2}{k}\)

\(\Rightarrow\left(1+\frac{1}{k-1}-\frac{1}{k}\right)^2=1+\frac{1}{\left(k-1\right)^2}+\frac{1}{k^2}\)

\(\Rightarrow\sqrt{1+\frac{1}{\left(k-1\right)^2}+\frac{1}{k^2}}=1+\frac{1}{k-1}+\frac{1}{k}\)

Cho \(k=3,4,...,2020.\)Ta có:

\(N=\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}+...+\sqrt{1+\frac{1}{2019^2}+\frac{1}{2020^2}}\)

\(=\left(1+\frac{1}{2}-\frac{1}{3}\right)+\left(1+\frac{1}{3}-\frac{1}{4}\right)+...+\left(1+\frac{1}{2018}-\frac{1}{2019}\right)+\left(1+\frac{1}{2019}-\frac{1}{2020}\right)\)

\(=2018+\frac{1}{2}-\frac{1}{2020}=2018\frac{1009}{2020}\)

Vậy \(N=2018\frac{1009}{2020}.\)

\(=\frac{2\left(\sqrt[3]{3}-1\right)}{\left(\sqrt[3]{3}-1\right)\left(\sqrt[3]{9}+\sqrt[3]{3}+1\right)}=\frac{2\left(\sqrt[3]{3}-1\right)}{3-1}=\frac{2\left(\sqrt[3]{3}-1\right)}{2}=\sqrt[3]{3}-1\)

Hồ Thu Giang nghe lời bn tốt, tui sẽ hạ nhiệt

Tên Cướp Mặt Trăng hì, tôi cx~ đùa thôi

Phạm Trần Trà My: Hạ nhiệt đi...

\(\frac{x-y}{\sqrt{x}-\sqrt{y}}-\frac{\sqrt{x^3}-\sqrt{y^3}}{x-y}=\frac{\left(x-y\right)\left(\sqrt{x}+\sqrt{y}\right)-x\sqrt{x}+y\sqrt{y}}{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}=\frac{x\sqrt{x}+x\sqrt{y}-y\sqrt{x}-y\sqrt{y}-x\sqrt{x}+y\sqrt{y}}{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}\)

\(=\frac{x\sqrt{y}-y\sqrt{x}}{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}=\frac{\sqrt{x}\sqrt{y}\left(\sqrt{x}-\sqrt{y}\right)}{\left(\sqrt{x-\sqrt{y}}\right)\left(\sqrt{x}+\sqrt{y}\right)}=\frac{\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\)