Question

Cum se rezolva ecuația ?

Answer 1

$(x - \frac{2}{3})^{2} + 3 = x - ( \frac{1}{3} - x)(x + \frac{4}{3}) \\ \\ {x}^{2} - 2x \times \frac{2}{3} + {( \frac{2}{3}) }^{2} + 3 = x - ( \frac{1}{3}x + \frac{1}{3} \times \frac{4}{3} - x \times x - \frac{4}{3}x) \\ \\ {x}^{2} - \frac{4}{3}x + \frac{4}{9} + 3 = x - ( \frac{1}{3}x + \frac{4}{9} - {x}^{2} - \frac{4}{3}x) \\ \\ {x}^{2} - \frac{4}{3}x + \frac{4}{9} + 3 = x - ( - x + \frac{4}{9} - {x}^{2}) \\ \\ {x}^{2} - \frac{4}{3}x + \frac{4}{9} + 3 = x + x - \frac{4}{9} + {x}^{2} \\ \\ - \frac{4}{3}x + \frac{4}{9} + 3 = x + x - \frac{4}{9} \\ \\ - \frac{4}{3}x + \frac{31}{9} = 2x - \frac{4}{9} \\ \\ 9( - \frac{4}{3}x + \frac{31}{9}) = 9(2x - \frac{4}{9}) \\ \\ - 9 \times \frac{4}{3}x + 9 \times \frac{31}{9} = 9 \times 2x - 9 \times \frac{4}{9} \\ \\ - 3 \times 4x + 31 = 18x - 4 \\ \\ - 12x + 31 = 18x - 4 \\ \\ - 12x - 18x + 31 = 18x - 18x - 4 \\ \\ - 12x - 18x + 31 = - 4 \\ \\ - 12x - 18x + 31 - 31 = - 4 - 31 \\ \\ - 12x - 18x = - 4 - 31 \\ \\ ( - 12 - 18)x = - (4 + 31) \\ \\ - 30x = - 35 \\ \\ - 30x : ( - 30) = - 35 : ( - 30) \\ \\ x = - 35 : ( - 30) \\ \\ x = 35 : 30 \\ \\ x = \frac{35}{30}^{(5} \\ \\ x = \frac{7}{6}$