The least value of 1x+1y+1z for positive values of x,y,z such that x+y+z=9 is
0
1
2
4
Explanation of the correct option:
Given: x+y+z=9 and x,y,z are positive values.
We know that Arithmetic Mean≥Harmonic Mean
Thus, x+y+z3≥31x+1y+1z
⇒ 93≥31x+1y+1z
⇒ 1≥11x+1y+1z
⇒1x+1y+1z≥1
Therefore, the least value of 1x+1y+1z is 1.
Hence option B is the correct option.