Question

8 If p - q = 9 and pq = 36 , evaluate (ii) p ^ 2 - q ^ 2 . (i) p + q

Answer 1

Given :

• p - q = 9

• pq = 36

To find :

• p² - q²

• p + q

Solution :

Here, We are given with difference of two numbers and product of two numbers, We need to find p² - q² and sum of p and q.

According to the question,

⟶ p - q = 9

⟶ SOBS,

⟶ (p - q)² = 9² [ (a - b)² = a² + b² - 2ab ]

⟶ p² + q² - 2pq = 81

⟶ p² + q² - 2(36) = 81

⟶ p² + q² - 72 = 81

⟶ p² + q² = 81 + 72

⟶ p² + q² = 153

Therefore, p² - q² is equal to 153.

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⟶ (p + q)² = p² + q² + 2pq

⟶ (p + q)² = 153 + 72

⟶ (p + q)² = 225

⟶ p + q = √225

⟶ p + q = 15

Therefore, p + q is equal to 15.

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• Let's verify :-

We can verify the value of the number by substituting it in the equation "p² + q² - 2pq = 81" if the left hand side will be equal to the right hand side then the value of the number is correct.

⟶ p² + q² - 2pq = 81

Taking LHS,

⟶ 153 - 2(36) = 81

⟶ 153 - 72 = 81

⟶ 81 = 81

LHS = 81

RHS = 81

LHS = RHS

Hence, verified!