Question

Show that the equation (x² + 1)²-x²=0 has no real roots.

Answer 1

hope this will help u... :-)

Answer 2

Answer:

-3

Step-by-step explanation:

Given that

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

Solution

$use \: here \: (a + b {)}^{2} = {a}^{2} + 2ab + {b}^{2}$

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

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

let

${x}^{2} = y$

${y}^{2} + y + 1 = 0$

now by discriminant formula

$d = {b}^{2} - 4ac$

$d = 1 - 4 \times 1 \times 1$

$d = - 3$