Question

Resolva em r as equações:
a) (x-5)²=64

b) (y+3)²=100​

Answer 1

a) (x-5)²=64

(x - 5).(x - 5) = 64

x² - 10x + 25 = 64

x² - 10x + 25 - 64 = 0

x² - 10x - 39 = 0

 

Δ = b² - 4.a.c

Δ = (-10)² - 4.1.(-39)

Δ = 100 + 156

Δ = 256

x = - b ± √Δ/2.a

x = 10 ± √256/2.1

x = 10 ± 16/2

$x'=\frac{10+16}{2}=13$  ou  $x''=\frac{10-16}{2}=-3$

S = {-3, 13}

_________________________________________________________

b) (y+3)²=100​

(y + 3).(y + 3) = 100

y² + 6y + 9 = 100

y² + 6y + 9 - 100 = 0

x² + 6y - 91 = 0

Δ = b² - 4.a.c

Δ = 6² - 4.1.(-91)

Δ = 36 + 364

Δ = 400

x = - b ± √Δ/2.a

x = - 6 ± √400/2.1

x = - 6 ± 20/2

$x'=\frac{-6+20}{2}=7$  ou  $x''=\frac{-6-20}{2}=-13$

S = {-13, 7}