If $α, β$ are the roots of the equation $x^{2} - 4 x + 1 = 0$ where $α < β$ then the number of real solutions of the equation $α^{y^{2} - 2 y + 1} + β^{y^{2} - 2 y - 1} = \frac{101}{10 β}$ are

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answer is 2.

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Detailed Solution

$α = 2 + \sqrt{3} β = 2 - \sqrt{3} \frac{{(2 + \sqrt{2})}^{y^{2} - 2 y}}{2 - \sqrt{3}} + \frac{{(2 - \sqrt{3})}^{y^{2} - 2 y}}{2 - \sqrt{3}} - \frac{101}{10 (2 - \sqrt{3})}$

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