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Home / 2r + 2 = (3 - \sqrt{5})r - 3 + \sqrt{5}

2r + 2 = (3 - \sqrt{5})r - 3 + \sqrt{5}

February 22, 2026

$2r + 2 = (3 - \sqrt{5})r - 3 + \sqrt{5}$

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Similarly:
2(r+1) = (3 - \sqrt{5})(r - 1)
2r + 2 = (3 - \sqrt{5})r - (3 - \sqrt{5})
2r - (3 - \sqrt{5})r + 5 - \sqrt{5} = 0
r = rac{\sqrt{5} - 5}{-1 + \sqrt{5}} = rac{-(5 - \sqrt{5})}{\sqrt{5} - 1}
Multiply numerator and denominator by \(\sqrt{5} + 1\):

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