Question

(p+q) (p²-pq+q²) verify it for p=3
q=2
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Answer 1

Answer:

p + q = 3

Subtract q from both sides:

p = 3-q

Now substitute for p in the second equation:

p^2 - q^2 = 15

p = 3-q

(3-q)^2 - q^2 = 15

Expand the parentheses on the left, and then use the FOIL method to distribute the terms:

(3-q)(3-q)-q^2 = 15

9 - 6q + q^2 - q^2= 15

Handily, both of the q^2’s cancel out:

9–6q = 15

Subtract 9 from both sides:

-6q = 6

Divide by -6:

q = -1

If q = -1, then if p = 3-q:

p = 3-q

q = -1

p = 3 - (-1)

p = 3 +1

p = 4

So p = 4 and q = -1. Let’s double-check these work by substituting for p and q in both of the original equations.

p + q = 3

p = 4

q = -1

4 + (-1) = 3

4 - 1 = 3

3 = 3

p^2 - q^2 = 15

p = 4

q = -1

4^4 - (-1)^2 = 15

16 - 1 = 15

15 = 15

So p = 4 and q = -1.

Answer 2

Answer:

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