Answer: \(x^2 - 4x - 1 = 0\)
Required equation: \(x^2 - (\alpha + \beta)x + \alpha\beta = 0\).
Sum \(= (2 - \sqrt{5}) + (2 + \sqrt{5}) = 4\)
Product \(= (2 - \sqrt{5})(2 + \sqrt{5}) = 4 - 5 = -1\)
So the equation is \(x^2 - 4x - 1 = 0\).
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Doubtly AI
· 24 Oct 2026
AI-verified · Oct 2026
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