If x+y+z=1 and x,y, z are positive real numbers, least value of 1/x+1/y+1/z

Answers (1)

We ; ; know ; ; that; ; Airthmetic ; Meangeq Harmonic; mean

Rightarrow fracfrac1x+frac1y+frac1z3geq frac3x+y+z

Rightarrow frac1x+frac1y+frac1zgeq frac9x+y+z

Rightarrow frac1x+frac1y+frac1zgeq 9; ; ; ; ; ; ; ; ; ; ; ; ; ; (ecause x+y+z=1)

So least value is 9

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