Question

Determinati x e R stiind ca x, (x-1)^2 si x+2 sunt in progresie aritmetica.

Answer 1

x, (x-1)^2 si x+2 sunt in progresie aritmetica==>

${(x - 1)}^{2} = \frac{x + x + 2}{2}$

(medie aritmetică )

${x}^{2} - 2x + 1 = \frac{2x + 2}{2} \\ {x}^{2} - 2x + 1 \frac{2 \times (x + 1)}{2} \\ {x}^{2} - 2x + 1 = x + 1 \\ {x}^{2} - 2x - x + 1 = 1 \\ {x}^{2} - 3 x + 1 - 1 = 0 \\ x \times (x - 3) = 0 \\ x = 0 \: sau \: x - 3 = 0 \\ x = 0 \: sau \: x = 0 + 3 \\ x = 0 \: sau \: x = 3$

x={0;3}

…ᘛ⁐̤ᕐᐷฅ^•ﻌ•^ฅ