Question

Let `x^2-3x+p=0` has two positive roots a and b, the minimum value of `((4)/(a)+(1)/(b))` is ____________.

Answer 1

Correct Answer - 3
a + b = 3
H.M `ge` A.M for numbe `(a)/(2), (a)/(2)`, b. We have
`(3)/((2)/(a) + (2)/(a) + (1)/(b)) le ((a)/(2) + (a)/(2) + 6)/(3) = 1`
`:. 1 ge (3)/((2)/(a) + (2)/(a) + (1)/(b))`or `(2)/(a) + (2)/(a) + (1)/(b) ge 3`
`:. (4)/(a) + (1)/(b) ge 3`