Question

What does the following equation represent? Explain.
p2 + 2 pq + q2 = 1

Answer 1

Answer:

The equation follows one of the algebraic identity; (a+b)^2=a^2+2ab+b^2

Answer 2

The given equation represent by (p + q + 1)(p + q - 1) = 0.

Explanation:

We have,

$p^2+2pq+q^2 = 1$

To find, the value of $p^2+2pq+q^2 = 1$.

∴ $p^2+2pq+q^2 = 1$

By factorisation method,

⇒ $p^2+pq+pq+q^2 = 1$

⇒ p(p + q) + q(p + q) = 1

⇒ (p + q)(p + q) = 1

⇒ $(p + q)^2= 1$

⇒ $(p + q)^2-1=0$

⇒ $(p + q)^2-1^2=0$

Using the algebraic identity,

$a^{2} -b^{2} =(a+b)(a-b)$

⇒ (p + q + 1)(p + q - 1) = 0

∴ The given equation represent by (p + q + 1)(p + q - 1) = 0.