If x2 + 4y2 + 2x + 1 = 0, then find the value of x39 + y36.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. −1.
Given that, x2 + 4y2 + 2x + 1 = 0
⇒ (x2 + 2x + 1) + 4y2 = 0
⇒ (x + 1)2 + 4y2 = 0
Now, (x + 1)2 > 0 and 4y2 > 0, the only solution is,
(x + 1)2 = 0
⇒ x = -1
Also, 4y2 = 0
⇒ y = 0
So, x39 + y36
⇒ (-1)39 + (0)36
⇒ -1 + 0 = -1
Hence the required answer is -1.