Question

A razão da PG 2, x+3, 5x+3) é?

Answer 1

primeiro vamos saber qual o valor de x

(x+3)/2 = (5x+3)/(x+3)

2(5x+3)=(x+3)(x+3)

10x+6=x²+2.3.x+3²
10x+6=x²+6x+9
x²+6x+9-6-10x=0
x²-4x+3=0

Δ=b²-4ac
Δ=(-4)-4.1.3
Δ=16-12
Δ=4

x=-b±√Δ /2a
x=-(-4)±√4 /2.1
x=4±2 /2

x'=4+2 /2
x'=6/2
x'=3

x"=4-2 /2
x"=2/2
x"=1

→para x=3

(2, x+3, 5x+3)
(2, 3+3 , 5.3+3)
(2,6, 15+3)
→PG=(2,6,18) q=6/2 = 3 (razao)

→para x=1

2, x+3, 5x+3
2, 1+3, 5.1+3
→PG=(2,4,8) q=4/2 = 2 (razao)

espero ter ajudado