Question : If $x^{2}+y^{2}+2x+1=0$, then the value of $x^{31}+y^{35}$ is:
Option 1: –1
Option 2: 0
Option 3: 1
Option 4: 2
Correct Answer: –1
Solution :
Given:
$x^{2}+y^{2}+2x+1=0$
⇒ $x^{2}+2x+1+y^{2}=0$
⇒ $(x+1)^2+y^2=0$
Since the addition of the squares of the two terms is zero,
So, both the terms are individually zero.
Therefore, $(x+1)^2=0$ and $y^2=0$.
⇒ $x=-1$ and $y=0$
Now, $x^{31}+y^{35}$
= $(-1)^{31}+(0)^{35}$
= –1
Hence, the correct answer is –1.
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