Question

Find one value of x that is a solution to the equation (x^2+3)^2=4x^2+12

Answer 1

`{( {x}^(2) + 3) }^(2) = {4x}^(2) + 12`

`\bf \purple{ {(x + y)}^(2) = {x}^(2) + 2xy + {y}^(2) }`

`{( {x}^(2)) }^(2) + 2({x)}^(2) (3) + {(3)}^(2) = {4x}^(2) + 12`

`{x}^(4) + {6x}^(2) + 9 = {4x}^(2) + 12`

`{x}^(4) = {4x}^(2) - {6x}^(2) + 12 - 9`

`{x}^(4) = { - 2x}^(2) + 3`

`( {x}^(2) * {x}^(2)) = { - 2x}^(2) + 3`

`2 * {x}^(2) = { - 2x}^(2) + 3`

`= \frac{ { - 2x}^(2) + 3 }{ {2x}^(2) }`

`= 3`

Answer 2

-1 or 1

Explanation: