if 3p - 2q = 10 and pq = -1, then find the value of 9p^2 + 4q^2
Answers
Answered by
9
Required Answer:-
Given:
- 3p - 2q = 10
- pq = -1
To find:
- The value of 9p² + 4q²
Solution:
We have,
➡ pq = -1
➡ 3p - 2q = 10
➡ (3p - 2q)² = 10² (Squaring both sides)
➡ (3p)² + (2q)² - 2 × 3p × 2q = 100 (Using identity (a - b)² = a² - 2ab + b²)
➡ 9p² + 4q² - 12pq = 100
➡ 9p² + 4q² - 12 × (-1) = 100
➡ 9p² + 4q² + 12 = 100
➡ 9p² + 4q² = 100 - 12
➡ 9p² + 4q² = 88
★ Hence, the value of 9p² + 4q² is 88.
Answer:
- 9p² + 4q² = 88
Identity Used:
- (a - b)² = a² - 2ab + b²
More Identities:
- (a + b)² = a² + 2ab + b²
- a² - b² = (a + b)(a - b)
- (a + b)³ = a³ + 3a²b + 3ab² + b³
- (a - b)³ = a³ - 3a²b + 3ab² - b³
Similar questions