Question

If 4a2 + 9b2 + 16c2 =2(3ab + 6bc + 4ca), then cosa

Answer 1

Answer:

CosA = -11/24

Step-by-step explanation:

4a² + 9b² + 16c² =2(3ab + 6bc + 4ca)

multiply by 2 both sides

=> 2(4a² + 9b² + 16c²) = 2 * 2(3ab + 6bc + 4ca)

=> 4a² + 9b² + 16c² + 4a² + 9b² + 16c² = 2*2*3ab + 2 * 2* 6bc  + 2 * 2 * 4ca

=> 4a² + 9b² - 2*2*3ab +  16c² + 4a² -  2 * 2 * 4ca + 9b² + 16c² -  2 * 2* 6bc = 0

=> (2a)² + (3b)² - 2*(2a)*(3b) + (4c)² + (2a)² - 2(4c)(2a) + (3b)² + (4c)² - 2 *(3b)(4c) = 0

=> (2a - 3b)² + (4c - 2a)² + (3b - 4c)² = 0

=> 2a = 3b   ,  2a = 4c    & 3b = 4c

=> 2a = 3b = 4c

Let say 2a = 3b = 4c = 12k

=> a = 6k   . b = 4k  , c = 3k

a² = b² + c² - 2bcCosA

=> (6k)² = (4k)² + (3k)² - 2*4k*3kCosA

=> 36k² = 16k² + 9k²  - 24k²CosA

=> 11k² =  - 24k²CosA

=> CosA = -11/24