Question

maior raiz da equação x2 - 5x + 4 = 0​

Answer 1

$\sf\:x {}^{2} - 5x + 4 = 0 \\ \\ \\ \sf\:x = - \frac{ - 5}{2} \pm \sqrt{\Bigg( \frac{ -5 }{2} \Bigg) {}^{2} - 4} \\ \\ \\ \sf\:x = \frac{5}{2} \pm \sqrt{\Bigg( \frac{ - 5}{2} \Bigg) {}^{2} - 4 } \\ \\ \\ \sf\:x = \frac{5}{2} \pm \sqrt{ \frac{ - 5 {}^{2} }{2 {}^{2} } - 4 } \\ \\ \\ \sf\:x = \frac{5}{2} \pm \sqrt{ \frac{25}{2 {}^{2} } - 4 } \\ \\ \\ \sf\:x = \frac{5}{2} \pm \sqrt{ \frac{25}{4} - 4} \\ \\ \\ \sf\:x = \frac{5}{2} \pm \sqrt{ \frac{25}{4} - \frac{4}{1} } \\ \\ \\ \sf\:x = \frac{5}{2} \pm \sqrt{ \frac{25 - 4 \cdot4}{4} } \\ \\ \\ \sf\:x = \frac{5}{2} \pm \sqrt{ \frac{25 - 16}{4} } \\ \\ \\ \sf\:x = \frac{5}{2} \pm \sqrt{ \frac{9}{4} } \\ 2\\ \\ \sf\:x = \frac{5}{2 } \pm \frac{ \sqrt{9} }{ \sqrt{4} } \\ \\ \\ \sf\:x = \frac{5}{2} \pm \frac{ \sqrt{3 {}^{2} } }{ \sqrt{4} } \\ \\ \\ \sf\:x = \frac{5}{2} \pm \frac{ \sqrt{3 {}^{2} } }{ \sqrt{2 {}^{2} } } \\ \\ \\ \sf\:x = \frac{5}{2} \pm \frac{3}{2} \\ \\ \\ \sf\:x _{2} = \frac{5}{2} + \frac{3}{2} \\ \\ \sf\:x _{1} = \frac{5}{2} - \frac{3}{2} \\ \\ \sf\:x = \frac{5 + 3}{2} \\ \\ \sf\:x _{2} = \frac{8}{2} \\ \\ \\ \sf\:x _{2} = 4 \\ \\ \\ \sf\: x_{1} = \frac{5 - 3}{2} \\ \\ \\ \sf\:x_{1} = \frac{2}{2} \\ \\ \\ \sf\:x _{1} = 1 \\ \\ \\ \\ \\ \\ \sf\:Sol:\Bigg \{x _{1} = 1, x_{2} = 4 \Bigg \}$

● Maior Raiz:

4

Att: Nerd1990