Question : If $x^2+8 y^2-12 y-4 x y+9=0$, then the value of $(7x-8y)$ is:
Option 1: 21
Option 2: 5
Option 3: 12
Option 4: 9
Correct Answer: 9
Solution : According to the question, ⇒ $x^2+8 y^2-12 y-4 x y+9=0$ ⇒ $x^2 - 4xy + 4y^2 + 4y^2 - 12y + 9 = 0$ ⇒ $(x - 2y)^2 + (2y - 3)^2 = 0$ ⇒ $x - 2y = 0, 2y - 3 = 0$ ⇒ $x = 2y, 2y = 3$ ⇒ $x = 3, y = \frac{3}{2}$ Now, $7x - 8y$ = 7 × (3) – 8 × $\frac{(3)}{2}$ = 21 – 12 = 9 Hence, the correct answer is 9.
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