Question

determine os valores de x que satisfazem cada equação a seguir: (x-4)^2=25 / (x+7)^2=9 / (x-2)^2=36 / (x+3)^2=16

Answer 1

1) (x-4)²=25
x²-8x+16=25
x²-8x+16-25=0
x²-8x-9=0
Δ=64+36
Δ=100
x = – b ± √Δ / 2a
x = 8±√100 / 2(1)
x = 8±10/2
x1 = 8+10/2 = 18/2 = 9
x2 = 8-10/2 = -2/2 = -1

2) (x+7)²=9
x²+14x+49=9
x²+14x+49-9=0
x²+14x+40=0
Δ=196-160
Δ=36

x = – b ± √Δ / 2a
x = - 14 ± 6 / 2
x1 = -14 + 6 / 2 = -8/2 = -4
x2 = -14 - 6 / 2 = -20/2 = -10

3) (x-2)²=36
x²-4x+4=36
x²-4x+4-36=0
x²-4x-32=0
Δ=16+128
Δ=144
x = – b ± √Δ / 2a
x = 4 ± 12 / 2
x1 = (4+12)/2=16/2= 8
x2=(4-12)/2=-8/2= -4

4)(x+3)²=16
x²+6x+9=16
x²+6x+9-16=0
x²+6x-7=0
Δ=36+28
Δ=64
x = – b ± √Δ / 2a
x = - 6 ± 8 / 2
x1 = -6+8/2 = 2/2 = 1
x2 = -6-8/2 = -14/2 = -7