Let a=x^2 + 4. Rewrite the following equation in terms of a and set it equal to zero. (x^2+4)^2+32=12x^2+48

Question

In resulting equation what is the coefficient of the a term? ______ in the resulting equation, what is the constant? _____ Show your work

Answer 1

To rewrite the given equation in terms of "a", substitute a = x^2 + 4:

((x^2 + 4)^2 + 32) = 12x^2 + 48
(a^2 + 32) = 12(x^2 - 4)

Now, expand the square of a:

a^2 + 32 = 12(x^2 - 4)

Now, let's isolate a. The coefficient of the a term is 1 and the constant is 32.