Question

4-Encontre a solução das seguintes inequações: a) x² -5x +4> 0 b) 2x² + 4x-6 ​

Answer 1

$a) x^2 -5x+4=0\\\\a=1\\b=-5\\c=4\\\\x= \frac{-b+-\sqrt{b^2-4ac}}{2a }\\x= \frac{-(-5)+-\sqrt{(-5)^2-4.1.4} }{2.1} \\\\x=\frac{5+-\sqrt{25-16} }{2} \\\\x=\frac{5+-\sqrt{3^2} }{2} \\\\x^1 = \frac{5+3}{2} = \frac{8}{2} =\frac{4}{1} = 4\\\\x^2=\frac{5-3}{2} = \frac{2}{2} = 1\\\\S=(1,4)$

$b)2x^2+4x-6=0\\\\a=2\\b=4\\c=-6\\\\x=\frac{-b+-\sqrt{b^2-4ac} }{2a} \\\\x=\frac{-4+-\sqrt{4^2-4.2.-6} }{2.2} \\\\x=\frac{-4+-\sqrt{16-8.-6} }{4} \\\\x=\frac{-4+-\sqrt{16+48} }{4} \\\\x=\frac{-4+-\sqrt{64} }{4} \\\\x= \frac{-4+-\sqrt{8^2} }{4} \\\\x^1=\frac{-4+8}{4} =\frac{4}{4} = \frac{1}{1} = 1\\ \\ x^2 = \frac{-4-8}{4} =\frac{-12}{4} = \frac{-3}{1} = -3\\\\S=(-3,1)$

os $x^1$ e $x^2$ são as raízes, ou, possíveis resultados de x, formando a Solução, representada pelo $S$