Question

Deterinar x a fim de que a sequencia (5x+1, x+1, x-2,) seja uma P.G.

Answer 1

( x + 1 )²  = ( 5x + 1 ) ( x - 2)
x² + 2x + 1 = 5x² - 10x + 1x - 2
x² - 5x² + 2x + 10x - 1x + 1 + 2 = 0
- 4x²  + 11x + 3 = 0   (-1)
4x² - 11x - 3 = 0
a = 4
b = - 11
c = - 3
Δ = b² - 4 ac
Δ = ( -11)² - 4 .4 . - 3
Δ = 121  + 48
Δ = 169
x = - b + - √Δ /2a
x = - ( - 11) + - √169 /2.4
x = 11 + - 13 / 8
x'  = 24/8 ⇒ x' = 3
x" = - 2/8 ⇒ x" = - 1/4

x= 3

PG = ( 5x + 1 , x + 1, x - 2 )
PG = ( 5.3 + 1, 3 + 1 , 3 - 2 )
PG = ( 16 , 4 , 1 )