Question : If $m+n=1$, then the value of $m^{3}+n^{3}+3mn$ is equal to:
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: 3
Answer (1)
19th Jan, 2024
Correct Answer: 1
Solution :
Given: $m+n=1$
Cubing both sides, we get
$(m+n)^3=1^3$
⇒ $m^3+n^3+3mn(m+n)=1$
Putting the value of $(m+n)$
⇒ $m^3+n^3+3mn(1)=1$
Thus, $m^3+n^3+3mn=1$
Hence, the correct answer is 1.
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