Question

Which equation is equivalent to
f(x) = 16x^4 – 81 = 0?

Answer 1

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

Step-by-step explanation: I got it right on the assignment

Answer 2

Explanation:

I'm pretty sure you are looking for factored forms as an equivalent equation, so here is how you do it.

This equation would be solved by difference of squares. 16, x^4, and 81 are all perfect squares ( which means that it is a number multiplied by itself, 16 is 4 x4 for example). So the first thing you want to do is recall the formula which is

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

(16x^4 - 81)= 0

Find the sq. root of 16 which is 4, and of x^4 which is x^2, and 81 which is 9. Now re write it in the (a - b)*(a + b) format. ----> (4x^2 - 9)*(4x^2 + 9) = 0