Question

Como se resolve esta equação ??

a) x² - 5x + 4 = 0

Answer 1

$x^2-5x+4=0~~~\Rightarrow~~\left\{ \!\begin{array}{l} a=1\\b=-5\\c=4 \end{array} \right.\\\\\\ \Delta=b^2-4ac\\\\ \Delta=(-5)^2-4\cdot 1\cdot 4\\\\ \Delta=25-16\\\\ \Delta=9\\\\\\ x=\dfrac{-b\pm \sqrt{\Delta}}{2a}\\\\\\ x=\dfrac{-(-5)\pm \sqrt{9}}{2\cdot 1}\\\\\\ x=\dfrac{5\pm 3}{2}$

$\begin{array}{rcl} x=\dfrac{5-3}{2}&~\text{ ou }~&x=\dfrac{5+3}{2}\\\\ x=\dfrac{2}{2}&~\text{ ou }~&x=\dfrac{8}{2}\\\\ x=1&~\text{ ou }~&x=4 \end{array}$


Conjunto solução: S = {1,  4}.


Bons estudos! :-)

Answer 2

x² - 5x + 4 = 0
a = 1; b = - 5; c = 4

Δ = b² - 4ac
Δ = (-5)² - 4.1.4
Δ = 25 - 16
Δ = 9

x = - b +/- √Δ     = - (-5) +/- √9
      ---------------     ------------------
            2a                   2.1

x' = 5 + 3
      ---------  = 8/2 = 4
          2

x" = 5 - 3
      --------  = 2/2 = 1
          2

R.: x = 4 e x = 1