19:
Xét ΔABC có
\(\dfrac{AB}{sinC}=\dfrac{AC}{sinB}\)
=>\(\dfrac{24}{sin25}=\dfrac{AC}{sin55}\)
=>\(AC=\dfrac{24}{sin25}\cdot sin55\simeq46,52\left(cm\right)\)
12:
a: \(A=\left(\dfrac{\sqrt{a}-1}{3\sqrt{a}-1}-\dfrac{1}{3\sqrt{a}+1}+\dfrac{8\sqrt{a}}{9a-1}\right):\left(1-\dfrac{3\sqrt{a}-2}{3\sqrt{a}+1}\right)\)
\(=\left(\dfrac{\sqrt{a}-1}{3\sqrt{a}-1}-\dfrac{1}{3\sqrt{a}+1}+\dfrac{8\sqrt{a}}{\left(3\sqrt{a}-1\right)\left(3\sqrt{a}+1\right)}\right):\dfrac{3\sqrt{a}+1-3\sqrt{a}+2}{3\sqrt{a}+1}\)
\(=\dfrac{\left(\sqrt{a}-1\right)\left(3\sqrt{a}+1\right)-3\sqrt{a}+1+8\sqrt{a}}{\left(3\sqrt{a}-1\right)\left(3\sqrt{a}+1\right)}\cdot\dfrac{3\sqrt{a}+1}{3}\)
\(=\dfrac{3a+\sqrt{a}-3\sqrt{a}-1+5\sqrt{a}+1}{3\sqrt{a}-1}\cdot\dfrac{1}{3}\)
\(=\dfrac{3a+3\sqrt{a}}{3\left(3\sqrt{a}-1\right)}=\dfrac{a+\sqrt{a}}{3\sqrt{a}-1}\)
b: A=3/2
=>\(\dfrac{a+\sqrt{a}}{3\sqrt{a}-1}=\dfrac{3}{2}\)
=>\(2a+2\sqrt{a}=9\sqrt{a}-3\)
=>\(2a-7\sqrt{a}+3=0\)
=>\(\left(\sqrt{a}-3\right)\left(2\sqrt{a}-1\right)=0\)
=>a=1/4(nhận) hoặc a=9(nhận)
