If $$8x^2 + y^2 - 12x - 4xy + 9 = 0$$, then the value of $$(14x - 5y)$$ is:

$$8x^2 + y^2 - 12x - 4xy + 9 = 0$$

$$4x^2 - 4xy + y^2 + 4x^2 - 12x + 9 = 0$$

$$[(2x)^2 - 2\times2x \times y + (y)^2] + [(2x)^2 - 2\times2x \times 3 + (3)^2] = 0$$
$$[2x - y]^2 + [2x - 3]^2 = 0$$

$$[2x - 3]^2 = 0$$

2x - 3 = 0

2x = 3

x = 1.5

$$[2x - y]^2 = 0$$

2x - y = 0

put the value of x in the above equation.

$$2\times1.5 - y = 0$$

3 - y = 0

y = 3

Value of $$(14x - 5y)$$ = $$(14\times1.5 - 5\times3)$$

= (21-15)

= 6