If 9(a² + b² ) + c² + 20 = 12(a + 2b), then the value of √(6a+9b+2c) is:

If 9(a² + b² ) + c² + 20 = 12(a + 2b), then the value of…

If 9(a² + b² ) + c² + 20 = 12(a + 2b), then the value of $\sqrt{6a+9b+2c}$ is:

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 4

9(a² + b²) + c² + 20 = 12(a + 2b)

9a² + 9b² + c² + 20 = 12a + 24b

9a² - 12a + 9b² - 24b + c² + 20 = 0

9a² - 12a + 4 + 9b² - 24b + 16 + c² = 0

(3a - 2)² + (3b - 4)² + c² = 0

(3a - 2) = 0

(3b - 4) = 0

c = 0

a = 2/3

b = 4/3

putting the value then we get,

(6 × 2/3 + 9 × 4/3)^1/2= 4