Question

${a}^{2} {x}^{2} - 2 {a}^{3}x + {a}^{4} + {c}^{2} = 0$
Solve the equation by factorization​

Answer 1

Answer:

$x = a - i \frac{c}{a} \: or \: a + i \frac{c}{a}$

Step-by-step explanation:

${a}^{2} {x}^{2} - 2 {a}^{3} x + {a}^{4} + {c}^{2} = 0$

${(ax)}^{2} - 2.ax. {a}^{2} + {( {a}^{2}) }^{2} + {c}^{2} = 0$

${(ax - {a}^{2} )}^{2} + {c}^{2} = 0$

${(ax - {a}^{2} )}^{2} - {i}^{2} {c}^{2} = 0$

$(ax - {a}^{2} + ic)(ax - {a}^{2} - ic) = 0$

$ax = {a}^{2} - ic \: or \: {a}^{2} + ic$

$x = a - i \frac{c}{a} \: or \: a + i \frac{c}{a}$