Minimum sum of reciprocals

If $x + y + z = 1$ , shew that the least value of $\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$ is 9.

~6 minProof · checked by AIInequalitiesAM-GM inequality

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIX. Inequalities, Examples XIX.b, No. 12 (part 1)

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