nhầm,giá trị nhỏ nhất nha

\(A=2x^2-4x+2xy+y^2+2003\)

\(=\left(x^2+2xy+y^2\right)+\left(x^2-4x+4\right)+2019\)

\(=\left(x+y\right)^2+\left(x-2\right)^2+2019\ge2019\)

(Dấu "="\(\Leftrightarrow x=2;y=-2\))

do AB/CD=MN/PQ => AB.PQ=MN.CD

TA CÓ: AB.PQ=MN.CD=>AB.PQ+CD.PQ=MN.CD+CD.PQ=>PQ(AB+CD)=CD(MN+PQ)=>AB+CD/CD=MN+PQ/PQ

TA CÓ: AB.PQ=MN.CD=>AB.PQ-CD.PQ=MN.CD-CD.PQ=>PQ(AB-CD)=CD(MN-PQ)=>AB-CD/CD=MN-PQ/PQ

NHỚ

\(ĐKXĐ:x\ne2\)

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

\(\Rightarrow\frac{\left(x-2\right)\left(x^2-4\right)}{x-2}+\frac{1}{x-2}=\frac{1}{2}\)

\(\Rightarrow\frac{x^3-2x^2-4x+8}{x-2}+\frac{1}{x-2}=\frac{1}{2}\)

\(\Rightarrow\frac{x^3-2x^2-4x+9}{x-2}=\frac{1}{2}\)

\(\Leftrightarrow2x^3-4x^2-8x+18=x-2\)

\(\Leftrightarrow2x^3-4x^2-9x+20=0\)

Đặt các giá trị:

\(\Delta=b^2-3ac=4^2-3.2.\left(-9\right)=70\)

\(k=\frac{9abc-2b^3-27a^2d}{2\sqrt{\left|\Delta\right|^3}}=\frac{-1384}{2\sqrt{70^3}}\)

\(\Delta>0\)và \(\left|k\right|>1\)Phương trình có ba nghiệm

Có hai nghiệm  là nghiệm phức nên ta loại

Vậy \(x=\frac{-2177}{1000}\)

\(\left(3x+2\right)^2-\left(x-3\right)^2=5x+8\)

\(\Leftrightarrow\left(3x+2+x-3\right)\left(3x+2-x+3\right)=5x+8\)

\(\Leftrightarrow\left(4x-1\right)\left(2x+5\right)=5x+8\)

\(\Leftrightarrow8x^2+18x-5=5x+8\)

\(\Leftrightarrow8x^2+13x-13=0\)

Ta có \(\Delta=13^2+4.8.13=585,\sqrt{\Delta}=3\sqrt{65}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{-13+3\sqrt{65}}{16}\\x=\frac{-3-3\sqrt{65}}{16}\end{cases}}\)

\(\frac{5x-3}{6}-\frac{7x-1}{4}-\frac{4x+2}{7}+5=0\)

<=> \(\frac{14\left(5x-3\right)-21\left(7x-1\right)-12\left(4x+2\right)+420}{84}=0\)

<=> 70x - 42 - 147x + 21 - 48x -24 + 420 = 0

<=> -125x + 375 = 0

<=> -125x = -375

<=> x = 3

Vậy S = {3}

\(\frac{3\left(2x+1\right)}{4}-5-\frac{3x+2}{10}=\frac{2\left(3x-1\right)}{5}\)

<=> \(\frac{15\left(2x+1\right)-100-2\left(3x+2\right)}{20}=\frac{8\left(3x-1\right)}{20}\)

<=> 30x + 15 - 100 - 6x - 4 = 24x - 8

<=> 24x - 24x = -8 + 89

<=> 0x = 81

=> pt vô nghiệm