Question

Resultado dessa equação x²-1=x+11

Answer 1

x² - 1 = x + 11 
x² - x - 12 = 0

Δ = b² - 4ac
Δ = (-1)² - 4(1)(-12)
Δ = 1 + 48
Δ = 49

x = (-b ± √∆)/2a
x = (1 ± √49)/2
x = (1 ± 7)/2
x' = 8/4 = 2
x'' = -6/2 = -3

Answer 2

Vamos Lá:

$x^2-1 = x+11$
$x^2-1-11-x = 0$
$x^2-12-x = 0$
$x^2-x-12 = 0$

$a = 1\\b =-1\\c=-12$

$\Delta = b^2-4ac$
$\Delta = -1^2 -4*1*-12$
$\Delta = 1+48$

$\Delta = 49$


$x = (-b\pm \sqrt{\Delta})/2a$
$x = (-(-1)\pm \sqrt{49})/2*1$
$x = (1\pm7)/2$

$x' = (1+7)/2$
$x' = 8/2$

$\boxed{x' = 4}$


$x" = (1-7)/2$
$x" = -6/2$

$\boxed{x" = -3}$

$\large\texttt{PROVA:}$

$x^2-1=x+11$
$x'^2-1= x'+11$
$4^2-1 = 4+11$
$16-1 = 4+11$
$15=15$

$x' = 4\\ \texttt{OK!}$


$x^2-1=x+11$
$x"^2-1 = x"+11$
$-3^2-1 = -3+11$
$9-1 = 8$

$8=8$

$x" = -3 \\ \texttt{OK!}$


$\large{S = \{(-3 ; 4)\}}$


Espero Ter Ajudado!!!
Bons Estudos!!!
:D