Question

Which equation is equivalent to

Answer 1

The answer is option 2.

Explanation:

In the question, 16 and 81 are perfect squares. So in order to find the equivalent equation, you have to factorize it :

APPLY,

`(a + b)(a - b) = {a}^(2) - {b}^(2)`

So for this question :

`16 {x}^(4) - 81 = 0`

`{(4 {x}^(2))}^(2) - {(9)}^(2)= 0`

`(4 {x}^(2) + 9)(4 {x}^(2) - 9) = 0`

Answer 2

(4x^2 +9)(4x^2-9) =0

Explanation:

16x^4 - 18 = 0

Rewriting

(4x^2)^2 - 9^2 =0

We notice that this is the difference of squares

a^2 - b^2 = (a-b)(a+b)

(4x^2 -9)(4x^2+9) =0