Question

como resolver
3(x-2)^2(x+5)=3(x+1)^2(x+1)+3

Answer 1

Explicación paso a paso:

$3( {x - 2})^{2} )(x + 5) = 3( {x - 1})^{2} (x + 1) + 3 \\ ( 3{x}^{2} - 12)(x + 5) = (3 {x}^{2} + 3)(x + 1) + 3 \\ 3 {x}^{3} + 15 {x}^{2} - 60 = 3( {x}^{3} + 3 {x}^{2} + 3x + 3 + 3 \\ 3 {x}^{3} + 15 {x}^{2} - 12x - 60 = 3 {x}^{3} + 3 {x}^{2} + 3x + 6 \\ 12 {x}^{2} - 15x - 66 = 0$

$12 {x}^{2} \div 3 - 15x \div 3 - 66 \div 3 = 0\\ 4 {x}^{2} - 5x - 22 = 0$

$x1 = \frac{ - ( - 5) + \sqrt{ {5}^{2} - 4(4)( -22)} }{2(4)} \\ x1 = \frac{ + 5 + \sqrt{25 + 352} }{8} \\ x1 = \frac{5 + 19.42}{8} \\ x1 = \frac{24.42}{8} = 3.0525 = 3$

$x2 = \frac{5 - \sqrt{ {5}^{2} - 4(4)( - 22) } }{2(4)} \\ x2 = \frac{5 - \sqrt{25 + 352} }{8} \\ x2 = \frac{5 - 19.42}{8} \\ x2 = \frac{ - 14.42}{8} \\ x2 = - 1.8025$