numerele x ; y si z sunt in prog. aritm . daca : y = ( x +z) / 2
sau 2y = x + z
a. daca 4√3 x - 5 = ( 2√3x - 6 + √3x + 1) /2
2 · 4√3x - 2·5 = 2√3x - 6 +√3x + 1
8√3x - 10 = 3√3x - 5
8√3x - 3√3x = 10 - 5
5√3x = 5
√3x = 1 ; x =1 /√3 = √3 /3
b. 2 · ( -3) /2 = 2x² - 3 + 5x + 2
- 3 = 2x² + 5x - 1
0 = 2x² + 5x - 1 + 3
2x² + 5x + 2 = 0 ; Δ =25 - 4 ·2·2 = 9 ; √Δ = √9 = 3
x₁ =( - 5 - 3) / 4 = - 8 / 4 = - 2 x₂ = ( - 5 + 3) / 4 = - 2 / 4 = -1 /2
doua progresii : 5 ; - 3 / 2 ; - 8 - 5 /2 ; - 3 /2 ; - 1 / 2
