a) \(\frac{-2}{5}+\frac{5}{6}.x=\frac{-4}{15}\)

\(\frac{5}{6}.x=\frac{-4}{15}-\frac{-2}{5}\)

\(\frac{5}{6}.x=\frac{2}{15}\)

\(x=\frac{2}{15}:\frac{5}{6}\)

\(x=\frac{4}{25}\)

b) \(\left(x-\frac{1}{5}\right)\left(y+\frac{1}{2}\right)\left(z-3\right)=0\)

\(x-\frac{1}{5}=0\)

\(x=0+\frac{1}{5}\)

\(x=\frac{1}{5}\)

Ta có

\(\begin{cases}\left|x-\frac{1}{2}\right|\ge0\\\left|y+\frac{3}{2}\right|\ge0\\\left|x+y-z-\frac{1}{2}\right|\ge0\end{cases}\)

Maf \(\left|x-\frac{1}{2}\right|+\left|y+\frac{3}{2}\right|+\left|x+y-z-\frac{1}{2}\right|=0\)

\(\Rightarrow\begin{cases}x-\frac{1}{2}=0\\y+\frac{3}{2}=0\\x+y-z-\frac{1}{2}=0\end{cases}\)

\(\Rightarrow\begin{cases}x=\frac{1}{2}\\y=-\frac{3}{2}\\x+y-z=\frac{1}{2}\end{cases}\)

\(\Rightarrow\begin{cases}x=\frac{1}{2}\\y=-\frac{3}{2}\\\frac{1}{2}-\frac{3}{2}-z=\frac{1}{2}\end{cases}\)

\(\Rightarrow\begin{cases}x=\frac{1}{2}\\y=-\frac{3}{2}\\-z=\frac{3}{2}\end{cases}\)

\(\Rightarrow\begin{cases}x=\frac{1}{2}\\y=-\frac{3}{2}\\z=-\frac{3}{2}\end{cases}\)

mk thấy chỉ cần 1 dữ kiện là tìm được x,y,z rùi

      x + y = y - 1 = z + 1

=>  x + y - y = -1 = z + 1

=> x = -1 = z + 1

=> x = -1

z + 1 = -1     => z = -2

y - 1 = z + 1

=> y - z = 1 + 1 = 2

=> y - (-2) = 2          => y + 2 = 2        => y = 2 - 2 = 0

Câu a:

- 2/3.(x -1/4) = 1/3.(2x + 1)

- 2/3x + 1/6 = 2/3x + 1/3

2/3x + 2/3x = 1/6 - 1/3

4/3x = 1/6 - 2/6

4/3x = - 1/6

x = -1/6 : 4/3

x = -1/8

Vậy x = - 1/8

Câu c:

(x -y^2 + z)^2 + (y - 2)^2 + (z + 3)^2 = 0 (1)

Vì : (x - y^2 + z)^2 ≥ 0 ∀ x; y; (y - 2)^2 ≥ 0 ∀ x; (z + 3)^2 ≥ 0 ∀ z

Nên (1) xảy ra khi cà chỉ khi:

x - y^2 + z = 0 (1) ; y - 2 = 0 và z + 3 = 0

y - 2 = 0

y =2

z + 3 = 0

z =- 3

Thay y = 2; z = - 3 vào (1) ta có:

x - 4 - 3 = 0

x = 4 + 3

x = 7

Vậy (x; y; z) = (7; 2; -3)