11.(y+3)=5.y+105

=>11.y+3=5.y+105

=>(11.y).(5.y)=105-3

=>(11.5)y=102

55y=102

y=102/55

b) 11.(y-6)=(4.y)+11

=>11y-6=4y+11

=>44y=11+6

44y=17

y=17/44

Áp dụng tc dtsbn:

\(\dfrac{x}{3}=\dfrac{y}{4};\dfrac{y}{5}=\dfrac{z}{7}\Leftrightarrow\dfrac{x}{15}=\dfrac{y}{20}=\dfrac{z}{28}=\dfrac{2x+3y-z}{30+60-28}=\dfrac{186}{62}=3\\ \Leftrightarrow\left\{{}\begin{matrix}x=45\\y=60\end{matrix}\right.\\ \Leftrightarrow x+y=105\left(C\right)\)

\(\frac{x}{2}=\frac{y}{3}=>\frac{x}{6}=\frac{y}{9}\)

\(\frac{x}{3}=\frac{z}{5}=>\frac{x}{6}=\frac{z}{10}\)

Vì vậy \(\frac{x}{6}=\frac{y}{9}=\frac{z}{10}\)

áp dụng tính chất dãy tỉ số bằng nhau:

...........................................................

(phần này bạn tự làm ha dễ mà)

a) \(77^2+23^2+77\cdot46\)

\(=77^2+2\cdot77\cdot23+23^2\)

\(=\left(77+23\right)^2\)

\(=100^2\)

\(=10000\)

b) \(105^2-5^2\)

\(=\left(105-5\right)\left(105+5\right)\)

\(=100\cdot110\)

\(=11000\)

c) \(A=\left(x-y\right)\left(x^2+xy+y^2\right)+2y^3\)

\(\Rightarrow A=x^3+y^3+2y^3\)

\(\Rightarrow A=x^3+3y^3\)

Thay \(x=\dfrac{2}{3};y=\dfrac{1}{3}\) vào \(A\), ta có:

\(A=\left(\dfrac{2}{3}\right)^3+3\cdot\left(\dfrac{1}{3}\right)^3\)

\(\Rightarrow A=\dfrac{8}{27}+\dfrac{3}{27}\)

\(\Rightarrow A=\dfrac{11}{27}\)

\(\dfrac{1}{5}+y=7\)

       \(y=7-\dfrac{1}{5}\)

      \(y=\dfrac{35}{5}-\dfrac{1}{5}\)

      \(y=\dfrac{34}{5}\)

_________________________

\(y:\dfrac{3}{4}=\dfrac{5}{7}\)

\(y=\dfrac{5}{7}\times\dfrac{3}{4}\)

\(y=\dfrac{15}{28}\)

Chúc bạn học tốt

\(\dfrac{1}{5}+Y=7\\ Y=7-\dfrac{1}{5}\\ Y=\dfrac{35}{5}-\dfrac{1}{5}\\ Y=\dfrac{34}{5}\)

\(Y\div\dfrac{3}{4}=\dfrac{5}{7}\\ Y=\dfrac{5}{7}\times\dfrac{3}{4}\\ Y=\dfrac{15}{28}\)

\(19+68+\left(y-19\right)=105\)

        \(68+y=105\)

                \(y=105-68\)

                \(y=37\)

Chúc bạn học tốt

Ta có: \(\frac{5x}{2}=\frac{6y}{5}=\frac{7z}{3}\) => \(\frac{x}{\frac{2}{5}}=\frac{y}{\frac{5}{6}}=\frac{z}{\frac{3}{7}}\)

Áp dụng t/c của dãy tỉ số bằng nhau, ta có:

 \(\frac{x}{\frac{2}{5}}=\frac{y}{\frac{5}{6}}=\frac{z}{\frac{3}{7}}=\frac{y-x-z}{\frac{5}{6}-\frac{2}{5}-\frac{3}{7}}=\frac{\frac{1}{105}}{\frac{1}{210}}=2\)

=> \(\hept{\begin{cases}\frac{x}{\frac{2}{5}}=2\\\frac{y}{\frac{5}{6}}=2\\\frac{z}{\frac{3}{7}}=2\end{cases}}\) => \(\hept{\begin{cases}x=\frac{4}{5}\\y=\frac{5}{3}\\z=\frac{6}{7}\end{cases}}\)

a, 10 - 2 x ( x - 1 ) = 44 

           2 x ( x - 1 ) = 10 - 44

           2 x ( x - 1 ) = -34 

                   x - 1 = -34 : 2 

                   x - 1 = -17

                   x      = -17 + 1 

                   x      = -16

Vậy x =-16

b, ( x + 2 ) x 3 - 10 = 5

    ( x + 2 ) x 3 = 5 + 10 

    ( x + 2 ) x 3 = 15

      x + 2 = 15 : 3 

      x + 2 = 5 

            x = 5 - 2 

            x = 3 

Vậy x = 3

c, x - 105 : 5 = 10 

    x - 105 = 10 x 5 

     x - 105 = 50

              x = 50 + 105

              x = 155

Vậy x = 155