Question

Determinati numerele intregi x,y stiind ca,in fiecare caz,numerele date sunt,in ordinea indicata,in progresie geometrica:
a)x-1 , x+1 , 4x+1
b)y , y+1 , y+3

Answer 1

a)$x+1= \sqrt{(x-1)(4x+1)} \\ (x+1)^2=(x-1)(4x+1) \\ x^{2} +2x+1=4 x^{2} -3x-1 \\ 3 x^{2} -5x-2=0$
Δ=49
$x_{1}= \frac{5+7}{6}=2; x_{2}= \frac{5-7}{2}=-1$
$b) (y+1)^{2}= y(y+3) \\ y^{2}+2y+1= y^{2}+3y \\ y=1$