Question

How many roots the quadratic equation (x^2+1)^2-x^2=0 has?

Answer 1

Answer:

The equation is

($x^{2}$ +1$)^{2}$ - $x^{2}$ = 0

$x^{4}$+ $1^{2}$ +2$x^{2}$  - $x^{2}$  = 0

$x^{4}$+ $1^{2}$ + $x^{2}$  = 0

$x^{4}$+ $x^{2}$  = -1

$x^{2}$($x^{2}$ +1) = -1

$x^{2}$ = -1,   ($x^{2}$ +1) = -1

$x$  = - 1,    $x^{2}$ +1= -1

$x$  = - 1,    $x^{2}$ = -1-1

              $x^{2}$ = -1-1

              $x^{2}$ = -2

              x = - $\sqrt{2}$

The equation has four roots -1, 1, $\sqrt{2}$ and  - $\sqrt{2}$

I hope it helped you.

thank you