Question

Como resolve?
a) x² - 8 = x/3
b) x (x - 2) = 2 (x+6)
c) (x+3)² = 12 - x²
d) x/2 - x/2 = -1/9

Answer 1

a) $x^{2} - 8 = \frac{x}{3}$ → Multiplica cruzado e você vai achar:
$3x^{2} -24 = x$ → $3x^{2} -x - 24=0$
a= 3 b= -1 c= -24
Δ= $b^{2} - 4ac$ 
Δ=  (-1)² - 4 ×3 × (-24)
Δ= 1 + 288
Δ= 289

x= $\frac{-b+- \sqrt{Δ} }{2a}$
x= $\frac{1+-17}{6}$
x1= $\frac{18}{6}=3$
x2= $\frac{-16}{6}$

S={ -$\frac{16}{6}$, 3}

b) x(x-2) = 2(x+6)
$x^{2} - 2x = 2x + 12$
$x^{2} - 2x -2x -12 = 0$ → $x^{2} -4x -12 =0$
a= 1 b=-4 c= -12
Δ = 16+ 48
Δ= 64
x1= $\frac{4+8}{2} = 6$
x2= $\frac{4-8}{2} = -2$

S= { -2, 6}

c) (x+3)² = 12 -$x^{2}$
$x^{2} + 2$ × x × 3 + $3^{2}$ = 12 -