Question

x³-12x²+38x-36=0 solve this equation​

Answer 1

${x}^{3} - 12 {x}^{2} + 38x - 36 = 0$

${x}^{3} - 2 {x}^{2} - 10 {x}^{2} + 20x + 18x - 36 = 0$

${x}^{2} (x - 2) - 10x(x - 2) + 18(x - 2) = 0$

$(x - 2)( {x}^{2} - 10x + 18) = 0$

$(x - 2) = 0 \: \: \: \: ∨ \: \: \: ({x}^{2} - 10x + 18 )= 0$

$x = 2 \: \: \: \: ∨ \: \: \: \: x = 5 \pm \sqrt{7}$

Therefore, the Solutions of the given cubic equation are:

$x_{1} = 2$

$x_{2} = 5 + \sqrt{7}$

$x _{3} = 5 - \sqrt{7}$