Question

For which of the following pairs (x,y)(x,y) does the inequality 12x^2 + 6y^2 \geq 17xy12x2+6y2≥17xy fail?​

Answer 1

=(3x - 2y( (4x - 3y)

Explanation:

We have,

12x2 – 17xy + 6y2

The coefficient of x2 is 12

The coefficient of x is -17y

Constant term is 6y2

So, we express the middle term -17xy as -9xy – 8xy

12x2 -17xy+ 6y2 = 12x2 – 9xy – 8xy + 6y2

= 3x (4x – 3y) – 2y (4x – 3y)

= (3x – 2y) (4x – 3y)