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Question: If a + b = 4 and ab = 3 then the value of \(\frac{\alpha}{\beta}\) + \(\frac{\beta}{\alpha}\) is –...

If a + b = 4 and ab = 3 then the value of αβ\frac{\alpha}{\beta} + βα\frac{\beta}{\alpha} is –

A

2

B

5

C

103\frac{10}{3}

D

83\frac{8}{3}

Answer

103\frac{10}{3}

Explanation

Solution

αβ\frac{\alpha}{\beta} + βα\frac{\beta}{\alpha} = α2+β2αβ\frac{\alpha^{2} + \beta^{2}}{\alpha\beta}

= (α+β)2–2αβαβ\frac{(\alpha + \beta)^{2}–2\alpha\beta}{\alpha\beta} = 16–63\frac{16–6}{3} = 103\frac{10}{3}