Math, asked by ankitkuma81, 5 months ago

if 3p - 2q = 10 and pq = -1, then find the value of 9p^2 + 4q^2​

Answers

Answered by anindyaadhikari13
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
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