numerele a , b si c >0 sunt trei termeni consecutivi ai progresiei geometrice daca : b² = a × c
( x + 7) ² = ( 5 - x)(3x + 11)
x² + 14x + 49 = 15x - 3x² + 55 -11x
4x² + 10x - 6 = 0
2x² + 5x - 3 = 0
Δ =5² - 4×2×( -3) = 25 + 24= 49
x₁ = ( - 5 - 7) / 4 = -12 / 4 = - 3
prog.geom. 8 ; 4 ; 2 ratia = 1 /2
x₂ = ( - 5 + 7) / 4 = 2 /4 = 1 /2
prog. geom :9 /2 ; 17 / 2 ; 25 / 2
nu verifica cond . prog. geom 17² = 9 × 25 289 ≠ 225
