\(Ax^2+4Ax+5A-2x^2+7x-1=0\)
\(\left(A-2\right)x^2+\left(4A+7\right)x+5A-1=0\)
+A=2 => 15x +9 =0 => x =-3/5 (1)
+A khác 2 : PT có nghiệm khi :\(\Delta\ge0\Leftrightarrow\left(4A+7\right)^2+4\left(A-2\right)\left(1-5A\right)\ge0\)
16A2 +56A+49 -20A2 +44A -8 >/ 0 => 4A2 -100A -41 </ 0
=> \(\frac{25-3\sqrt{74}}{2}\le A\le\frac{25+3\sqrt{74}}{2}\)(2)
(1)(2) => \(\frac{25-3\sqrt{74}}{2}\le A\le\frac{25+3\sqrt{74}}{2}\)
=> A min=\(\frac{25-3\sqrt{74}}{2}\)
A max =\(\frac{25+3\sqrt{74}}{2}\)
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