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Question
The roots of the equation 2x2 – 7x + 5 = 0 are α and β. Without solving for the roots, find `alpha/beta + beta/alpha`
Solution
2x2 – 7x + 5 = `x^2 - 7/2x + 5/2` = 0
α + β = `7/2`
αβ = `5/2`
`alpha/beta + beta/alpha = (alpha^2 + beta^2)/(alphabeta)`
= `((alpha + beta)^2 - 2alphabeta)/(alphabeta)`
= `(alpha + beta)^2/(alphabeta) - 2`
= `(7/2)^2/(5/2) - 2`
= `49/4 xx 2/5 - 2`
= `49/10 - 2`
= `(49 - 20)/10`
= `29/10`
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