Bài 6 : Vì \(\left|x+\frac{23}{19}\right|\ge0\forall x\in Z\)

=> Để \(A=\left|x+\frac{23}{19}\right|\) nhận giá trị nhỏ nhất thì A = 0 \(\Leftrightarrow x=\frac{-23}{19}\)

Bài 7 : Vì \(\left|\frac{7}{9}-x\right|\ge0\forall x\)

 \(\Rightarrow C=-\left|\frac{7}{9}-x\right|\le0\forall x\)

=> Để \(C=-\left|\frac{7}{9}-x\right|\) nhận giá trị lớn nhất thì C = 0 \(\Leftrightarrow x=\frac{7}{9}\)

a. Vì \(\left|x+\frac{23}{19}\right|\ge0\forall x\in R\)

\(\Rightarrow A_{min}=0\Leftrightarrow x=\frac{-23}{19}\)

b. Vì \(-\left|\frac{7}{9}-x\right|\le0\forall x\in R\)

\(\Rightarrow C_{max}=0\Leftrightarrow x=\frac{7}{9}\)

Ta có: \(\frac{3^{31}.25^8-9^{14}.5^{15}}{27^{10}.5^{15}-3^{30}.5^{17}}=\frac{3^{31}.\left(5^2\right)^8-\left(3^2\right)^{14}.5^{15}}{\left(3^3\right)^{10}.5^{15}-3^{30}.5^{17}}=\frac{3^{31}.5^{16}-3^{28}.5^{15}}{3^{30}.5^{15}-3^{50}.5^{17}}\)

\(=\frac{5^{28}.5^{15}.\left(3^3.5-1\right)}{3^{30}.5^{15}.\left(1-5^2\right)}=\frac{135-1}{3.\left(-24\right)}=\frac{134}{-72}=-\frac{67}{36}\)

Ta có: \(\left(\frac{1}{16}\right)^x=\left(\frac{1}{2}\right)^{20}\) 

=> \(\left[\left(\frac{1}{2}\right)^4\right]^x=\left(\frac{1}{2}\right)^{20}\)

=> \(\left(\frac{1}{2}\right)^{4x}=\left(\frac{1}{2}\right)^{20}\)

=> 4x = 20

=> x = 20 : 4

=> x=  5

\(P=0,4\left(3\right)+0,6\left(2\right)\cdot2\frac{1}{2}-\frac{\frac{1}{2}+\frac{1}{3}}{0,5\left(8\right)}:\frac{50}{53}\)

\(\Rightarrow P=\frac{13}{30}+\frac{28}{45}\cdot\frac{5}{2}-\frac{3+2}{6}:\frac{53}{90}\cdot\frac{53}{50}\)

\(\Rightarrow P=\frac{13}{30}+\frac{14}{9}-\frac{5}{6}\cdot\frac{90}{53}\cdot\frac{53}{50}\)

\(\Rightarrow P=\frac{39}{90}+\frac{140}{90}-\frac{2}{3}\)

\(\Rightarrow\frac{179}{90}-\frac{60}{90}=\frac{119}{90}\)

\(\frac{\left[\left(5,2^2:2,6+8,1\right)^2-6,5^2\right]:0,025}{\left(60,192:2,4-1,08\right)^2-0,24.140}\)

\(=\frac{\left[\left(27,04:2,6+8,1\right)^2-42,25\right]:0,025}{\left(25,08-1,08\right)^2-336}\)

\(=\frac{\left[\left(10,4+8,1\right)^2-42,25\right]:0,025}{24^2-336}\)

\(=\frac{\left(18,5^2-42,25\right):0,025}{576-336}\)

\(=\frac{\left(342,25-42,25\right):0,025}{240}\)

\(=\frac{300:0,025}{240}=\frac{12000}{240}=50\)

a.

\(\hept{\begin{cases}x=\frac{-23}{68}=\frac{-23.172}{68.172}=\frac{-3956}{11696}\\y=\frac{-57}{172}=\frac{-57.58}{172.68}=\frac{-3306}{11696}\end{cases}\Leftrightarrow x>y}\)

b.

\(\hept{\begin{cases}x=\frac{-31}{33}=\frac{-31.51}{33.51}=\frac{-1581}{1683}\\y=\frac{-49.33}{51.33}=\frac{-1617}{1683}\end{cases}}\Leftrightarrow x>y\)

Sửa câu a: \(x< y\)

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

\(\frac{x}{6}=\frac{y}{9}=\frac{x-y}{6-9}=\frac{30}{-3}=-10\)

\(\Rightarrow x=-60;y=-90\)