ISI2016-MMA-17

Question

The number of positive integers $n$ for which $n^3 +(n+1)^3 +(n+2)^3 = (n+3)^3$ is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Comments

n³ + (n+1)³ + (n+2)³ = (n+3)³

n³ +( n³ + 3n² +3n +1)+(n³ + 6n² +12n +8)  = n³ + 9n² +27n +27

n³  - 6n -9=0

n(n²-6)=9

only n=3 satisfy above equation

Ans : B