If α and β are the roots of the equation x2 – 5x + 6 = 0, find (i) α2+β2 (ii) α/β +β/α

6. If  α  and β  are the roots of the equation x² – 5x + 6 = 0, find

(i) α²+β²

(ii) α/β +β/α

Sol. x² – 5x + 6 = 0

Comparing with ax² + bx + c = 0 we have a = 1, b = -5, c = 6

α and β are the roots of the given quadratic equation, [Given]

α + β  = ^-b/_a = -(-5)/1 = 5

Also, αβ = c/a = 6/1 = 6

(i) α²+β² = (α + β )² – 2αβ = 5² – 2 (6) = 25 – 12 = 13

(ii) α/β +β/α = (α² + β²)/ αβ = 13/6