b) \(\left|x-\frac{3}{4}\right|+\left|\frac{2}{5}-y\right|+\left|x-y+z\right|=0\)

\(\Leftrightarrow\hept{\begin{cases}x-\frac{3}{4}=0\\\frac{2}{5}-y=0\\x-y+z=0\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x=\frac{3}{4}\\y=\frac{2}{5}\\z=-\frac{7}{20}\end{cases}}\).

a), c) Tương tự. 

\(\frac{x}{y}=\frac{3}{4}\Leftrightarrow\frac{x}{3}=\frac{y}{4}\Leftrightarrow\frac{x}{15}=\frac{y}{20}\)

\(\frac{y}{z}=\frac{5}{7}\Leftrightarrow\frac{y}{5}=\frac{z}{7}\Leftrightarrow\frac{y}{20}=\frac{z}{28}\).

Suy ra \(\frac{x}{15}=\frac{y}{20}=\frac{z}{28}\).

Áp dụng tính chất dãy tỉ số bằng nhau ta có: 

\(\frac{x}{15}=\frac{y}{20}=\frac{z}{28}=\frac{2x+3y-z}{2.15+3.20-28}=\frac{186}{62}=3\)

\(\Leftrightarrow\hept{\begin{cases}x=3.15=45\\y=3.20=60\\z=3.28=84\end{cases}}\).

Bạn đăng tách ra để nhận được câu trả lời nhanh nhé. Vì do khá dài nên mình sẽ trả lời tách từng phần.

a) \(\left|x+\frac{1}{2}\right|+\left|y-\frac{3}{4}\right|+\left|z-1\right|=0\)

Ta có: \(\hept{\begin{cases}\left|x+\frac{1}{2}\right|\ge0\forall x\inℚ\\\left|y-\frac{3}{4}\right|\ge0\forall x\inℚ\\\left|z-1\right|\ge0\forall x\inℚ\end{cases}}\)

Mà đề ra: \(\left|x+\frac{1}{2}\right|+\left|y-\frac{3}{4}\right|+\left|z-1\right|=0\)

\(\Rightarrow\left|x+\frac{1}{2}\right|=0\Rightarrow x+\frac{1}{2}=0\Rightarrow x=\frac{-1}{2}\)

\(\Rightarrow\left|y-\frac{3}{4}\right|=0\Rightarrow y-\frac{3}{4}=0\Rightarrow y=\frac{3}{4}\)

\(\Rightarrow\left|z-1\right|=0\Rightarrow z-1=0\Rightarrow z=1\)

b) \(\left|x-\frac{3}{4}\right|+\left|\frac{2}{5}-y\right|+\left|x-y+z\right|=0\)

Ta có: \(\hept{\begin{cases}\left|x-\frac{3}{4}\right|\ge0\forall x\inℚ\\\left|\frac{2}{5}-y\right|\ge0\forall x\inℚ\\\left|x-y+z\right|\ge0\forall x\inℚ\end{cases}}\)

Mà đề ra: \(\left|x-\frac{3}{4}\right|+\left|\frac{2}{5}-y\right|+\left|x-y+z\right|=0\)

\(\Rightarrow\left|x-\frac{3}{4}\right|=0\Rightarrow x-\frac{3}{4}=0\Rightarrow x=\frac{3}{4}\)

\(\Rightarrow\left|\frac{2}{5}-y\right|=0\Rightarrow\frac{2}{5}-y=0\Rightarrow y=\frac{2}{5}\)

\(\Rightarrow\left|x-y+z\right|=0\Rightarrow x-y+z=0\Rightarrow\frac{3}{4}-\frac{2}{5}+z=0\Rightarrow z=\frac{-7}{20}\)

bài nào cx đc ngoại trừ bài 1

( 3x - 2 )² + 1,25 = 7,5

=> ( 3x - 2 )² = 6,25

\(\Rightarrow\left(3x-2\right)^2=\frac{25}{4}\)

\(\Rightarrow\left(3x-2\right)^2=\left(\frac{5}{2}\right)^2=\left(\frac{-5}{2}\right)^2\)

\(\Rightarrow\orbr{\begin{cases}3x-2=\frac{5}{2}\\3x-2=\frac{-5}{2}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}3x-2=\frac{5}{2}\\3x-2=\frac{-5}{2}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}3x=\frac{9}{2}\\3x=\frac{-1}{2}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{3}{2}\\x=\frac{-1}{6}\end{cases}}\)