Question : If $x + y = 1$, then what is the value of $x^3+ 3xy + y^3$?
Option 1: –1
Option 2: 1
Option 3: 0
Option 4: 2
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Correct Answer: 1
Solution :
Given: $x + y = 1$------------------ (equation 1)
We know the algebraic identity, $(x+y)^3=x^3 + y^3+3xy(x+y)$.
Substitute the value from equation (1) in the above formula,
$(1)^3=x^3 + y^3+3xy\times(1)$
⇒ $x^3 + y^3+3xy=1$
Hence, the correct answer is 1.
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