\(P=\frac{x+y}{xyz}=\frac{x}{xyz}+\frac{y}{xyz}=\frac{1}{yz}+\frac{1}{xz}\)

Áp dụng Bunyakovsky dạng phân thức : \(\frac{1}{yz}+\frac{1}{xz}\ge\frac{4}{z\left(x+y\right)}\)(1)

Ta có : \(\sqrt{z\left(x+y\right)}\le\frac{x+y+z}{2}\)( theo AM-GM )

=> \(z\left(x+y\right)\le\left(\frac{x+y+z}{2}\right)^2=\left(\frac{6}{2}\right)^2=9\)

=> \(\frac{1}{z\left(x+y\right)}\ge\frac{1}{9}\)=> \(\frac{4}{z\left(x+y\right)}\ge\frac{4}{9}\)(2)

Từ (1) và (2) => \(P=\frac{x+y}{xyz}=\frac{1}{yz}+\frac{1}{xz}\ge\frac{4}{z\left(x+y\right)}\ge\frac{4}{9}\)

=> P ≥ 4/9

Vậy MinP = 4/9, đạt được khi x = y = 3/2 ; z = 3

\(\frac{5x-1}{3}+\frac{7x-1,1}{3}-\frac{1,5-5x}{7}=\frac{9x-0,7}{4}\)

⇔ \(\frac{5x-1+7x-1,1}{3}-\frac{1,5-5x}{7}-\frac{9x-0,7}{4}=0\)

⇔ \(\frac{12x-2,1}{3}-\frac{1,5-5x}{7}-\frac{9x-0,7}{4}=0\)

⇔ \(\frac{28\left(12x-2,1\right)}{84}-\frac{12\left(1,5-5x\right)}{84}-\frac{21\left(9x-0,7\right)}{84}=0\)

⇔ \(\frac{336x-58,8}{84}-\frac{18-60x}{84}-\frac{189x-14,7}{84}=0\)

⇔ \(\frac{336x-58,8-18+60x-189x+14,7}{84}=0\)

⇔ \(\frac{207x-62,1}{84}=0\)

⇔ 207x - 62, 1 = 0

⇔ 207x = 62, 1

⇔ x = 0, 3

\(\frac{5x-1}{3}+\frac{7x-1.1}{3}-\frac{1.5-5x}{7}=\frac{9x-0,7}{4}\)

\(\Leftrightarrow\left(\frac{5x-1}{3}+\frac{7x-1.1}{3}\right)-\frac{1.5-5x}{7}=\frac{9x-0,7}{4}\)

\(\Leftrightarrow\left(\frac{5x-1+7x-1.1}{3}\right)-\frac{1.5-5x}{7}=\frac{9x-0,7}{4}\)

\(\Leftrightarrow\frac{12x-2.1}{3}-\frac{1.5-5x}{7}=\frac{9x-0,7}{4}\)

\(\Leftrightarrow\frac{28\left(12x-2.1\right)}{84}-\frac{12\left(1.5-5x\right)}{84}-\frac{21\left(8x-0,7\right)}{84}=0\)

\(\Leftrightarrow\frac{336x-58.8-18+60x-189x+14.7}{84}=0\)

\(\Leftrightarrow336x-58.8-18+60x-189x+14.7=0\)

\(\Leftrightarrow207x-62.1=0\)

\(\Leftrightarrow207x=62.1\)

\(\Leftrightarrow x=\frac{62.1}{207}=\frac{3}{10}=0.3\)

\(\frac{7x^2-14x-5}{15}=\frac{\left(2x+1\right)^2}{5}-\frac{\left(x-1\right)^2}{3}\)

=> \(\frac{7x^2-14x-5}{15}=\frac{3\left(2x+1\right)^2}{15}-\frac{5\left(x-1\right)^2}{15}\)

=> \(\frac{7x^2-14x-5}{15}=\frac{3\left(4x^2+4x+1\right)-5\left(x^2-2x+1\right)}{15}\)

=> \(\frac{7x^2-14x-5}{15}=\frac{7x^2+22x-2}{15}\)

=> 7x² - 14x - 5 = 7x² + 22x - 2

=> -14x - 5 + 22x - 2

=> 36x = -3

=> x = -1/12

\(\frac{7x^2-14x-5}{15}=\frac{\left(2x+1\right)^2}{5}-\frac{\left(x-1\right)^2}{3}\)

\(\Leftrightarrow\frac{7x^2-14x-5}{15}=\frac{4x^2+4x+1}{5}-\frac{x^2-2x+1}{3}\)

\(\Leftrightarrow\frac{7x^2-14x-5}{15}-\frac{4x^2+4x+1}{5}+\frac{x^2-2x+1}{3}=0\)

\(\Leftrightarrow\frac{7x^2-14x-5}{15}-\frac{3\left(4x^2+4x+1\right)}{15}+\frac{5\left(x^2-2x+1\right)}{14}=0\)

\(\Leftrightarrow7x^2-14x-5-12x^2-12x-3+5x^2-10x+5=0\)

\(\Leftrightarrow-36x-3=0\)

\(\Leftrightarrow-36x=3\)

\(\Leftrightarrow x=\frac{3}{-36}=-\frac{1}{12}\)

\(\frac{\left(x-2\right)\left(x+10\right)}{3}-\frac{\left(x+4\right)\left(x+10\right)}{12}=\frac{\left(x-2\right)\left(x+4\right)}{4}\)

<=> \(\frac{x^2+8x-20}{3}-\frac{x^2+14x+40}{12}-\frac{x^2+2x-8}{4}=0\)

<=> \(\frac{4\left(x^2+8x-20\right)}{12}-\frac{x^2+14x+40}{12}-\frac{3\left(x^2+2x-8\right)}{12}=0\)

<=> \(\frac{4x^2+32x-80}{12}-\frac{x^2+14x+40}{12}-\frac{3x^2+6x-24}{12}=0\)

<=> \(\frac{4x^2+32x-80-x^2-14x-40-3x^2-6x+24}{12}=0\)

<=> \(\frac{12x-96}{12}=0\)

<=> 12x - 96 = 0

<=> 12x = 96

<=> x = 8

\(\frac{\left(5x-1\right)\left(7x-1,1\right)}{3}-\frac{1,5-5x}{7}-\frac{9x-0,7}{4}=0\)

\(\frac{35-5,5x-7x-11}{3}-\frac{1,5-5x}{7}-\frac{9x-0,7}{4}=0\)

\(\frac{24-12,5x}{3}-\frac{1,5-5x}{7}-\frac{9x-0,7}{4}=0\)

\(\frac{28.\left(24-12,5x\right)-12.\left(1,5-5x\right)-21\left(9x-0,7\right)}{84}=0\)

\(\frac{672-350x-18+60x-189x+14,7}{84}=0\)

\(\frac{668,7-479x}{84}=0\)

=> \(\left(668,7-479x\right).\frac{1}{84}=0\)

\(668,7-479x=0\)

\(479x=668,7\)

\(x=139,47\)

Bài mk ko biết có đúng hay ko nữa :((

Sai thì thôi nhé nhớ giúp mk nhé cảm ơn bạn nhìu

\(\frac{x+1}{35}+\frac{x+3}{33}=\frac{x+5}{31}+\frac{x+7}{29}\Leftrightarrow\frac{x+1}{35}+1+\frac{x+3}{33}+1=\frac{x+5}{31}+1+\frac{x+7}{29}+1\)

\(\frac{x+36}{35}+\frac{x+36}{33}=\frac{x+36}{31}+\frac{x+36}{29}\Leftrightarrow\left(x+36\right)\left(\frac{1}{35}+\frac{1}{33}-\frac{1}{31}-\frac{1}{29}\right)=0\)

mà \(\frac{1}{35}+\frac{1}{33}-\frac{1}{31}-\frac{1}{29}\ne0\) vậy \(x+36=0\Rightarrow x=-36\)

\(\frac{x+1}{35}+\frac{x+3}{33}=\frac{x+5}{31}+\frac{x+7}{29}\)

\(\Leftrightarrow\frac{x+1}{35}+1+\frac{x+3}{33}+1=\frac{x+5}{31}+1+\frac{x+7}{29}+1\)

\(\Leftrightarrow\frac{x+36}{35}+\frac{x+36}{33}-\frac{x+36}{31}-\frac{x+36}{29}=0\)

\(\Leftrightarrow\left(x+36\right)\left(\frac{1}{35}+\frac{1}{33}-\frac{1}{31}-\frac{1}{29}\ne0\right)=0\)

\(\Leftrightarrow x=-36\)

\(\frac{\left(x-2\right)\left(x+10\right)}{3}-\frac{\left(x+4\right)\left(x+10\right)}{12}=\frac{\left(x-2\right)\left(x+4\right)}{4}\)

<=> \(\frac{4\left(x^2+10x-2x-20\right)-\left(x^2+10x+4x+40\right)}{12}=\frac{3\left(x^2+4x-2x-8\right)}{12}\)

=> \(4x^2+40x-8x-80-x^2-10x-4x-40=3x^2+12x-6x-24\)

<=> \(4x^2+40x-8x-80-x^2-10x-4x-40-3x^2-12x+6x+24=0\)

<=> \(12x-96=0\)

<=>\(12x=96\)

<=>\(x=8\)