Question

Find p + q If p2– q2 = 75 p - q = 2

Answer 1

Given,

p-q = 2

p2-q2 = 75

We know,

p2-q2 = (p+q).(p-q) ( here . means multiplication )

So,

(p+q).(p-q) = 75

(p+q).2 = 75 ( given in question that p-q = 2)

p+q = 75/2

Hope you have understood.

Answer 2

We shall solve this by using algebraic identity, which says

( x + a) ( x + b) = x^2 + ( a + b) x + ab

Generalizing the formula put, b = - a.

Now,

⇒(x+a) ( x - a)

⇒ x^2 + ( a - a) x + a(-a)

⇒ x^2 - a^2

So, We have generalized the formula,

(a + b) ( a - b) = a^2 - b^2.

We are given that,

⇒p² - q² = 75

⇒p - q = 2

So,

⇒p² - q² = ( p + q) ( p - q)

⇒75 = ( p + q) × 2

⇒75/2 = ( p + q).

Therefore, ( p + q) = 75/2.