Question

Resolva em seu caderno:
A) x^2-14x+49=0
B)4x^2-20x+25=0
C)4y^2=4y-1=0
D)p^2+6p=16p-25=0

Answer 1

A)

x² - 14x + 49 = 0

Δ = b² - 4.a.c
Δ = (-14)² - 4.1.49
Δ = 196 - 196
Δ = 0

x = -b ± √Δ / 2.a
x = 14 ± √0 / 2.1
x = 14 ± 0 / 2
x' = 14 + 0 / 2
x' = 14 / 2 = 7
x'' = 14 - 0 / 2
x'' = 14 / 2 = 7

B)
4x² - 20x + 25 = 0

Δ = b² - 4.a.c
Δ = ( -20)² - 4.4.25
Δ = 400 - 400
Δ = 0

x = -b ± √Δ / 2.a
x = 20 ± √0 / 2.4
x = 20 ± 0 / 8
x' = 20 / 8
x' = $\frac{2}{5}$
x'' = 20 - 0 / 8
x'' = 20 / 8 = $\frac{2}{5}$

C)
4y² = 4y - 1 = 0
4y² - 4y + 1 = 0

Δ = b² - 4.a.c
Δ = ( -4)² - 4.4.1
Δ = 16 - 16
Δ = 0

x = -b ± √Δ / 2.a
x = 4 ± √Δ / 2.a
x = 4 ± √0 / 2.4
x = 4 ± 0 / 8
x' = 4 + 0 / 8
x' = 4 / 8 = $\frac{1}{2}$
x'' = 4 - 0 / 8
x'' = 4 / 8 = $\frac{1}{2}$

D) 
p² + 6p = 16p - 25 = 0
p² + 6p - 16 + 25
p² - 10p + 25 = 0

Δ = b² - 4.a.c
Δ = ( - 10 )² - 4.1.25
Δ = 100 - 100
Δ = 0

x = -b ± √Δ / 2.a
x = 10 ± √0 / 2.1
x = 10 ± 0 / 2
x' = 10 + 0 / 2
x' e x'' = 5