(x³ + y³ + 1 - 3 xy) ÷ (x+y+1)
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Step-by-step explanation:
Let x+y=t
Cubing on both sides, we get
⇒(x+y)
3
=t
3
⇒x
3
+y
3
+3xy(x+y)=t
3
⇒x
3
+y
3
+3xyt=t
3
⇒x
3
+y
3
−t
3
=−3xyt
Substitute $$t=-1$, we get
⇒x
3
+y
3
−(−1)
3
=−3xy(−1)
⇒x
3
+y
3
+1=3xy which is the given equation
Therefore, x+y=t
⇒x+y=−1
⇒x+y+1=0
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