\(\left(x-3\right)\left(4x+5\right)+2019\)

\(=4x^2-7x-15+2019\)

\(=4x^2-7x+2004\)

\(=4\left(x^2-\frac{7}{4}x+501\right)\)

\(=4\left(x^2-\frac{7}{4}x+\frac{49}{64}+\frac{32015}{64}\right)\)

\(=4\left[\left(x-\frac{7}{8}\right)^2+\frac{32015}{64}\right]\)

\(=4\left[\left(x-\frac{7}{8}\right)^2\right]+\frac{32015}{16}\ge\frac{32015}{16}\)

Vậy GTNN của bt là \(\frac{32015}{16}\Leftrightarrow x-\frac{7}{8}=0\Leftrightarrow x=\frac{7}{8}\)

mk tưởng 7/4

A = \(\frac{\frac{3}{4}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{4}-\frac{5}{11}+\frac{5}{13}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}-\frac{5}{6}+\frac{5}{8}}\)

\(=\frac{3.\left(\frac{1}{4}-\frac{1}{11}+\frac{1}{13}\right)}{5.\left(\frac{1}{4}-\frac{1}{11}+\frac{1}{13}\right)}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{2}.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{4}\right)}\)

\(=\frac{3}{5}+\frac{1}{\frac{5}{2}}\)

\(=\frac{3}{5}+\frac{2}{5}=1\)

b) B = \(\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6.8^4.3^5}-\frac{5^{10}.7^3:25^5.49}{\left(125.7\right)^3+5^9.14^3}\)

\(=\frac{2^{12}.3^5-\left(2^2\right)^6.\left(3^2\right)^2}{2^{12}.3^6+\left(2^3\right)^4.3^5}-\frac{5^{10}.7^3-\left(5^2\right)^5.7^2}{\left(5^3\right)^3.7^3+5^9.\left(7.2\right)^3}\)

\(=\frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}-7^2}{5^9.7^3+5^9.7^3.2^3}\)

\(=\frac{2^{12}.3^4.\left(3-1\right)}{2^{12}.3^5\left(3+1\right)}-\frac{5^{10}.7^2.\left(7-1\right)}{5^9.7^3\left(1+2^3\right)}\)

 \(=\frac{1}{3.2}-\frac{5.2}{7.3}\)

\(=\frac{7}{3.2.7}-\frac{5.2.2}{7.3.2}\)

\(=\frac{7}{42}-\frac{20}{42}\)

\(=-\frac{13}{42}\)

Mình làm câu này  các câu khác tương tự 

Mấu chốt làm bài này là đưa về thừa số nguyên tố

\(\frac{12^7.3^{35}.14^{21}}{9^{21}.7^{21}.2^{35}}=\frac{3^7.4^7.3^{35}.2^{21}.7^{21}}{3^{2.21}.7^{21}.2^{35}}=\frac{3^7.2^{2.7}.3^{35}.2^{21}.7^{21}}{3^{2.21}.7^{21}.2^{35}}=\frac{3^7.2^{14}.3^{35}.2^{21}.7^{21}}{3^{42}.7^{21}.2^{35}}=\frac{3^{42}.2^{35}.7^{21}}{3^{42}.7^{21}.2^{35}}=1\)

Có 2 cách 

C1:  \(\frac{x}{21}=\frac{y}{14}\Rightarrow\frac{3x}{63}=\frac{7y}{98}=\frac{3x-7y}{63-98}=\frac{70}{-35}=-2\\ \)=> \(\hept{\begin{cases}3x=63.\left(-2\right)\\7y=98\left(-2\right)\end{cases}\Rightarrow\hept{\begin{cases}x=-42\\y=-28\end{cases}}}\)

C2

\(\frac{x}{21}=\frac{y}{14}\Rightarrow x=\frac{21}{14}y=\frac{3}{2}y\\ \)

Mà \(3x-7y=70\Rightarrow3.\frac{3}{2}y-7y=70\Rightarrow-\frac{5}{2}y=70\Rightarrow y=-28\Rightarrow x=-42\)