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Let alpha, beta be the roots of x^(2) +...

Let `alpha, beta ` be the roots of `x^(2) + bx + 1 = 0` . Them find the equation whose roots are `-(alpha + 1//beta) and -(beta + 1//alpha).`

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To find the equation whose roots are \(-(\alpha + \frac{1}{\beta})\) and \(-(\beta + \frac{1}{\alpha})\), where \(\alpha\) and \(\beta\) are the roots of the equation \(x^2 + bx + 1 = 0\), we will follow these steps: ### Step 1: Identify the relationships from the given quadratic equation From the equation \(x^2 + bx + 1 = 0\), we can use Vieta's formulas: - The sum of the roots \(\alpha + \beta = -b\) - The product of the roots \(\alpha \beta = 1\)
To find the equation whose roots are \(-(\alpha + \frac{1}{\beta})\) and \(-(\beta + \frac{1}{\alpha})\), where \(\alpha\) and \(\beta\) are the roots of the equation \(x^2 + bx + 1 = 0\), we will follow these steps: ### Step 1: Identify the relationships from the given quadratic equation From the equation \(x^2 + bx + 1 = 0\), we can use Vieta's formulas: - The sum of the roots \(\alpha + \beta = -b\) - The product of the roots \(\alpha \beta = 1\)
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