If x2 + 8y2 - 12y - 4xy + 9 = 0 , then the value of ( 7x - 8y) is :
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 9
x2 + 8y2 - 12y - 4xy + 9 = 0
(a + b)2 = a2 + b2 + 2ab
(a - b)2 = a2 + b2 - 2ab
⇒ x2 + 4y2 - 4xy + 4y2 + 9 - 12y= 0
⇒ (x - 2y)2 + (2y - 3)2 = 0
Here
2y - 3 = 0
y = 3/2
and x - 2y = 0
x = 2 × 3/2 = 3
Now the value of
7x - 8y = 7 × 3 - 8 × 3/2 = 9