2010-II-43 – Solving Master

Ans: B
Since

h

5

and

k

form an arithmetic sequence, then we have

$\begin{array}{rcl} h + k & = & 2 \times 5 \\ h + k & = & 10 \dots ① \end{array}$

Since $h$ , $4$ and $k$ form a geometric sequence, then we have

$\begin{array}{rcl} h k & = & 4^{2} \\ h k & = & 16 \dots ① \end{array}$

Hence by $①$ and $①$ , we have

$\begin{array}{rcl} (h + k)^{2} & = & 10^{2} \\ h^{2} + 2 h k + k^{2} & = & 100 \\ h^{2} + k^{2} + 2 (16) & = & 100 \\ h^{2} + k^{2} & = & 68 \end{array}$

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