Question

If x² + 8y² – 12y – 4xy + 9 = 0, find 15x – 4y 
1. 43
2. 29
3. 37
4. 39

Answer 1

Correct Answer - Option 4 : 39

Given:

x² + 8y² – 12y – 4xy + 9 = 0

Formula used:

(a – b)² = a² + b² – 2ab

Calculation:

According to the question,

⇒ x² + 8y² – 12y – 4xy + 9 = 0

⇒ x² + 4y² – 4xy + 4y² + 9 – 12y = 0

⇒ (x – 2y)² + (2y – 3)² = 0

As square cannot be negative,

⇒ x – 2y = 0

⇒ x = 2y

And,

⇒ 2y – 3 = 0

⇒ y = 3/2

⇒ x = 2(3/2)

⇒ x = 3

Putting the values of x and y in 15x – 4y

⇒ 15x – 4y = 15(3) – 4(3/2)

⇒ 15x – 4y = 45 – 6

⇒ 15x – 4y = 39

∴ The value of 15x – 4y is 39.