Question

Determine as raízes destas equações :
A) (x+3)² = 49
B) (5x-4)² = 9
C) (21x-7)² = 0

Answer 1

a)(x+3)²=49
(x+3)·(x+3)=49
x²+3x+3x+9=49
x²+6x+9-49=0
x²+6x-40=0
Δ=6²- 4·1·(-40)
Δ=36+160
Δ=196
$x=\frac{-6\pm\sqrt{196}}{2\cdot{1}}=\frac{-6\pm14}{2}$
x'=8/2⇒4
x"=-20/2⇒ - 10
b)(5x-4)²=9
(5x-4)·(5x-4)=9
25x²-20x-20x+16=9
25x²-40x+16-9=0
25x²-40x+7=0
Δ=(-40)²-4·25·7
Δ=1600-700
Δ=900
$x=\frac{-(-40)\pm\sqrt{900}}{2\cdot{25}}=\frac{40\pm30}{50}$
x'=70/50⇒7/5
x"=10/50⇒1/5
c)(21x-7)²=0
(21x-7)·(21x-7)=0
441x²-147x-147x+49=0
441x²-294x+49=0 (dividir por 49)
9x²-6x=0 (dividir por 3)
3x²-2x=0
Δ=(-2)²-4·3·0
Δ=4-0
Δ=4
$x=\frac{-(-2)\pm\sqrt{4}}{2\cdot{3}}=\frac{2\pm2}{6}$
x'=4/6⇒2/3
x"=0/6⇒0

Espero ter ajudado XD