Question : If $a+b=3$, then the value of $a^{3}+b^{3}+9ab-27$ is:
Option 1: 24
Option 2: 25
Option 3: 0
Option 4: 27
Answer (1)
25th Jan, 2024
Correct Answer: 0
Solution :
Given: $a+b=3$
Cubing both sides, we get
$(a+b)^3=3^3$
⇒ $a^3+b^3+3ab(a+b)=27$
Putting, $(a+b)=3$
⇒ $a^3+b^3+3ab×3=27$
⇒ $a^3+b^3+9ab=27$
Thus, $a^3+b^3+9ab–27=0$
Hence, the correct answer is 0.
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