Question
If x2 + y2 + 2x +1 = 0, then the value of x31 + y35 is?
Answer: Option A
$$\eqalign{
& {x^2} + {y^2} + 2x + 1 = 0 \cr
& \Rightarrow {\left( {x + 1} \right)^2} + {y^2} = 0 \cr
& {\text{Let }}{\left( {x + 1} \right)^2} = 0 \cr
& {y^2} = 0 \cr
& x = - 1,y = 0 \cr
& {\text{Now, }}{x^{31}} + {y^{35}} \cr
& = {\left( { - 1} \right)^{31}} + {\left( 0 \right)^{35}} \cr
& = - 1 \cr} $$
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$$\eqalign{
& {x^2} + {y^2} + 2x + 1 = 0 \cr
& \Rightarrow {\left( {x + 1} \right)^2} + {y^2} = 0 \cr
& {\text{Let }}{\left( {x + 1} \right)^2} = 0 \cr
& {y^2} = 0 \cr
& x = - 1,y = 0 \cr
& {\text{Now, }}{x^{31}} + {y^{35}} \cr
& = {\left( { - 1} \right)^{31}} + {\left( 0 \right)^{35}} \cr
& = - 1 \cr} $$
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