Question

Q. 23. Find the value of p² + q² when p-q = 7 and pq = 9.​

Answer 1

Solution:

Given,

→ p - q = 7

→ pq = 9

We have to find out the value of p² + q²

So, We know that,

→ (a - b)² = a² - 2ab + b²

So,

→ (p - q)² = p² - 2pq + q²

Putting the values, we get,

→ 7² = p² + q² - 2 × 9

→ 49 = p² + q² - 18

→ p² + q² = 67

★ So, the value of p² + q² is 67.

Answer:

• p² + q² = 67.

Additional Identities:

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• a² - b² = (a + b)(a - b)
• (a + b)² = (a - b)² + 4ab
• (a - b)² = (a + b)² - 4ab
• (a + b)³ = a³ + 3ab(a + b) + b³
• (a - b)³ = a³ - 3ab(a - b) - b³
• a³ + b³ = (a + b)(a² - ab + b²)
• a³ - b³ = (a - b)(a² + ab + b²)