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Question
Write the following expression in terms of α + β and αβ
`(alpha + 3)/beta + (beta + 3)/alpha`
Solution
`(alpha + 3)/beta + (beta + 3)/alpha = (alpha(alpha + 3) + beta(beta + 3))/(alphabeta)`
= `(alpha^2 + 3alpha + beta^2 + 3beta)/(alphabeta)`
= `(alpha^2 + beta^2 + 3alpha + 3beta)/(alphabeta)` ...[a2 + b2 = (a + b)2 – 2ab]
= `((alpha + beta)^2 - 2alphabeta + 3(alpha + beta))/(alphabeta)`
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