If $x^{2}+8y^{2}+12y-4xy+9 = 0$, then the value of $(7x + 8y)$ is :
Answer & explanation
Correct answer: option 3
Given,
x2 + 8y2 – 12y – 4xy + 9 = 0
We know that,
(a – b)2 = a2 + b2 – 2ab
x2 + 8y2 – 12y – 4xy + 9 = 0
⇒ x2 + 4y2 + 4y2 – 12y – 4xy + 9 = 0
⇒ (x2 + 4y2 – 4xy) + (4y2 – 12y + 9) = 0
⇒ (x – 2y)2 + (2y – 3)2 = 0
Now, 2y – 3 = 0
y = \(\frac{3}{2}\)
Put the value of y in x – 2y
x – 2 × \(\frac{3}{2}\) = 0
x = 3
$(7x + 8y)$ = 7× 3 + 8×\(\frac{3}{2}\)
$(7x + 8y)$ = 33