Question

Qual e o valor de x em 3x-1; 4x; x-5; para que seja uma PG

Answer 1

4x² = (3x -1) (x -5)
4x² = 3x² -15x -x +5 
x² +16x -5 = 0

Δ² = 16² -4 . 1 . -5
Δ² = 256 + 20
Δ = √276
Δ = 2√69

x = (-16 ± 2√69)/2

x' = ± -8√69

Answer 2

Olá grazyalves1413 ! ☺

Bem, siga o passo a passo da resolução abaixo:

$\displaystyle \mathsf {4x^2 = (3x -1) (x -5)}$

$\displaystyle \mathsf {4x^2= 3x^2 -15x -x +5}$ 

$\displaystyle \mathsf {x^2 +16x -5 = 0}$

$\displaystyle \mathsf {\Delta^2 = 16^2-4\cdot 1\cdot -5}$

$\displaystyle \mathsf {\Delta^2=256+20}$

$\displaystyle \mathsf {\Delta =\sqrt {276}}$

$\displaystyle \mathsf {\Delta=2\sqrt {69}}$

$\displaystyle \mathsf {x =\dfrac { (-16\pm 2\sqrt {69})}{2}}$

$\displaystyle \mathsf {x'=\pm-8\sqrt {69}}$