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Question Number 14365 by RasheedSindhi last updated on 31/May/17

Related to Q#14157  a^2 +b^2 −ab=α^2   b^2 +c^2 −bc=β^2   c^2 +d^2 −cd=γ^2   d^2 +e^2 −de=δ^2   e^2 +a^2 −ea=ξ^2

$$\mathrm{Related}\:\mathrm{to}\:\mathrm{Q}#\mathrm{14157} \\ $$$$\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} −\mathrm{ab}=\alpha^{\mathrm{2}} \\ $$$$\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} −\mathrm{bc}=\beta^{\mathrm{2}} \\ $$$$\mathrm{c}^{\mathrm{2}} +\mathrm{d}^{\mathrm{2}} −\mathrm{cd}=\gamma^{\mathrm{2}} \\ $$$$\mathrm{d}^{\mathrm{2}} +\mathrm{e}^{\mathrm{2}} −\mathrm{de}=\delta^{\mathrm{2}} \\ $$$$\mathrm{e}^{\mathrm{2}} +\mathrm{a}^{\mathrm{2}} −\mathrm{ea}=\xi^{\mathrm{2}} \\ $$

Commented by mrW1 last updated on 01/Jun/17

The solution is a pyramid with a  pentagon base whose other 5 side  areas are triangles with a top  angle of 60°.

$${The}\:{solution}\:{is}\:{a}\:{pyramid}\:{with}\:{a} \\ $$$${pentagon}\:{base}\:{whose}\:{other}\:\mathrm{5}\:{side} \\ $$$${areas}\:{are}\:{triangles}\:{with}\:{a}\:{top} \\ $$$${angle}\:{of}\:\mathrm{60}°. \\ $$

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