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Answer variants:
57
75
(α+β)22αβ+3(α+β)αβ
(α+β)2+2αβ3(α+β)αβ
75
(α+β)2+2αβ+3(α+β)αβ
1. Write the expression \(\frac{\alpha + 3}{\beta} + \frac{\beta + 3}{\alpha}\) in terms of \(\alpha + \beta\) and \(\alpha \beta\).
 
Answer:
 
The solution is
.
 
2. The roots of the equation \(2x^2 - 7x + 5 = 0\) are \(\alpha\) and \(\beta\). Without solving for the roots, find \(\frac{1}{\alpha} + \frac{1}{\beta}\).
 
Answer:
 
The value of \(\frac{1}{\alpha} + \frac{1}{\beta}\) is
.