Question

Поможіть будьласка з мене 20 балів

Answer 1

Ответ:

$5 {x}^{2} - 75 =5( {x}^{2} - 15) = 5(x - \sqrt{15} )(x + \sqrt{15} ) \\ 2 {x}^{2} - 12x + 18 = 2 {(x - 3)}^{2} \\ {x}^{4} + x = x( {x}^{3} + 1) = x(x + 1)( {x}^{2} - x + 1) \\ {x}^{5} - 8 {x}^{2} = {x}^{2} ( {x}^{3} - 8) = {x}^{2} (x - 2)( {x}^{2} + 2x + 4) \\ {a}^{2} - 9 {b}^{2} + 5a - 15b = (a - 3b)(a + 3b) + 5(a - 3b) = (a - 3b)(a + 3b + 5) \\ {p}^{2} - 2pq + {q}^{2} - 4 = {(p - q)}^{2} - 4 = (p - q - 2)(p - q + 2)$

${x}^{3} - 49x = 0 \\ x( {x}^{2} - 49) = 0 \\ x(x - 7)(x + 7) = 0 \\ x1 = 0 \\ x2 = 7 \\ x3 = - 7$

${x}^{3} + 8 {x}^{2} + 16x = 0 \\ x( {x}^{2} + 8x + 16) = 0 \\ x {(x + 4)}^{2} \\ x1 = 0 \\ x2 = - 4$

${y}^{3} - 8 {y}^{2} - y - 8 = 0 \\ {y}^{2} (y - 8) - y + 8 = 0 \\ {y}^{2} (y - 8) - (y - 8) = 0 \\ ( {y}^{2} - 1)(y - 8) = 0 \\ (y - 1)(y + 1)(y - 8) = 0 \\ y1 = 8 \\ y2 = 1 \\ y3 = - 1$