Question

Write the following expression in terms of α + β and αβ

`(alpha + 3)/beta + (beta + 3)/alpha`

Answer 1

`(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)`