Question

(x-1)(x-3)(x+5)(x+7)=297

Answer 1

Answer:

x=4

Step-by-step explanation:

(4-1)(4-3)(4+5)(4+7)=297

Answer 2

First simplify the expression into polynomial form,

$(x-1)(x-3)(x+5)(x+7)=297$

$x^4+8x^3-10x^2-104x+105=297$

$x^4+8x^3-10x^2-104x-192=0$

Now factor into,

$(x-4)(x+8)(x^2+4x+6)=0$

Which means the solutions are,

$x-4=0\implies\boxed{x_1=4}$

$x+8=0\implies\boxed{x_2=-8}$

and then two complex solutions because determinant of the third factor $D\lt0$,

$x^2+4x+6=0$

$x^2+4x+4=-2$

$(x+2)^2=-2\implies\boxed{x_3=i\sqrt{2}-2},\boxed{x_4=-i\sqrt{2}-2}$

Hope this helps :)