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
In resulting equation what is the coefficient of the a term?
In the resulting equation, what is the constant?
First, let's rewrite the equation in terms of a:
a^2 + 32 = 12a + 48
Next, rearrange the equation by moving everything to one side:
a^2 - 12a + 16 = 0
Now, the resulting equation is a quadratic equation in terms of a. The coefficient of the a term is -12 and the constant term is 16.
are you sure
I apologize for the mistake in my previous response. Let's correct that.
The correct equation in terms of a is:
a^2 + 32 = 12a + 48
Substitute a = x^2 + 4 back into this equation:
(x^2 + 4)^2 + 32 = 12(x^2 + 4) + 48
Expanding and simplifying:
x^4 + 8x^2 + 16 + 32 = 12x^2 + 48
x^4 + 8x^2 + 48 = 12x^2 + 48
x^4 - 4x^2 = 0
This equation is now in terms of x, so there is no a term. The constant term is 0. Thank you for pointing that out, and I apologize for the error in my initial response.