Respuesta :
Answer:
p = 2, q = 3.
Step-by-step explanation:
First, let's expand the brackets on the right side using the identity that (a-b)^2 = a^2-2ab+b^2 -> x^2-4x+1 = x^2-2px+p^2-q
The x^2 cancels out, and we're left with -4x+1 = -2px+p^2-q.
Now, basically just by matching up the two sides of the equation, let's set up a system of equations to find p and q. -4x+1 = -2px+p^2-q, here it looks like -2p = -4. Also, it looks like p^2-q = 1.
From the first equation, dividing both sides by -2, we get p = 2. Plugging this into the second equation, 2^2-q = 4-q = 1, then subtracting 4 from both sides, we get -q = 1-4 = -3, which is the same as saying q = 3.
Therefore, p = 2, q = 3.
