Question

2x(x−26)2−x2(x−26)=0

Answer 1

Ответ:

$2x(x - 26)2 - {x}^{2} (x - 26) = 0 \\ 4x(x - 26) - {x}^{3} + 26 {x}^{2} = 0 \\ 4 {x}^{2} - 104x - {x}^{3} + 26 {x}^{2} = 0 \\ - {x}^{3} + 30 {x}^{2} - 104x = 0 \\ - x( {x}^{2} - 30x + 104) = 0 \\ 1) - x = 0 \\ x = 0 \\ 2) {x}^{2} - 30x + 104 = 0 \\ d = {b}^{2} - 4ac = {( - 30)}^{2} - 4 \times 1 \times 104 = 900 - 416 = 484 \\ x1 = \frac{ -b - \sqrt{d} }{2a} = \frac{ - ( - 30) - \sqrt{484} }{2 \times 1} = \frac{30 - 22}{2} = \frac{8}{2} = 4 \\ x2 = \frac{ -b + \sqrt{d} }{2a} = \frac{ - ( - 30) + \sqrt{484} }{2 \times 1} = \frac{30 + 22}{2} = \frac{52}{2} = 26$