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
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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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