tmua.me Tau Paper 2 · Question 5

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tmua.me Tau Paper 2 · Q5

Paper 2Powers & logarithmsAlgebra

For real $k$ , let $N(k)$ be the number of ordered triples $(x,y,z)$ of pairwise distinct positive real numbers, none equal to $1$ , for which

xyz=1,\qquad x+y+z=6,

(\log_x y)^2+(\log_y z)^2+(\log_z x)^2=k.

What is the complete set of values of $k$ for which $N(k)=6$ ?

[5,21/4]

\{5\}

\{21/4\}

\{9/2,5\}

\{5,21/4\}

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