Question

. Determine a raiz da equação: 4 + x ( x - 4 ) = x

Answer 1

4 + x ( x - 4) = x
4 + x² - 4x = x
x² - 4x + 4 = x
x² -4x -x + 4 = 0
x² - 5x + 4 = 0

a = 1
b = -5
c = 4

Δ = b² - 4 .a .c 
Δ = (-5)² -4 . 1 . 4
Δ = 25 - 4 . 4 
Δ = 25 - 16
Δ = 9


$\mathtt{\dfrac{-b +-\sqrt{\Delta }}{2~.~a}~~=~~ \dfrac{- (-5) +- \sqrt{9}}{2~.~1}~~=~~ \dfrac{5 +- ~3}{2}} \\ \\ \\ \mathtt{x' = \dfrac{5 + 3}{2}~~=~~ \dfrac{8}{2}~~=~~4} \\ \\ \\ \mathtt{x'' = \dfrac{5 - 3}{2} ~~=~~\dfrac{2}{2}~~=~~1}$

Resposta: { 1 e 4 }

Answer 2

Olá!!!

Resolução!!!

4 + x ( x - 4 ) = x
4 + x² - 4x = x
4 + x² - 4x - x = 0
x² - 4x - x + 4 = 0
x² - 5x + 4 = 0

x² - 5x + 4 = 0

a = 1, b = - 5, c = 4

∆ = b² - 4ac
∆ = ( - 5 )² - 4 • 1 • 4
∆ = 25 - 16
∆ = 9

x = - b ± √∆ / 2a
x = - ( - 5 ) ± √9 / 2 • 1
x = 5 ± 3 / 2
x' = 5 + 3 / 2 = 8/2 = 4
x" = 5 - 3 / 2 = 2/2 = 1

S = { 1, 4 }

Espero ter ajudado!!!