The numerator of a fraction is a multiple of two nos. One of the nos. is greater
than other by 2. The greater no. is smaller than the denominator by 1. If the
denominator is given as 5 + c (c is a constant), then the minimum value of the
fraction is
(a) 2
(b) –2
(c) –1/2
(d) 1/2
The fraction can be written as F = (4 + c) (2 + c) / (5 + c)
Put 5 + c = t or c = t – 5
∴ F = (t – 3) (t – 1)/t
= (t^2 – rt + 3)/t
= (t^2 – 4t + 4 – 1)/t
= (t – 2)^2/ t – 1/t
Hence, the given expression is minimum, if the square term is equal to zero
∴(t-2)/t = 0 or t = 2
Hence answer is A
than other by 2. The greater no. is smaller than the denominator by 1. If the
denominator is given as 5 + c (c is a constant), then the minimum value of the
fraction is
(a) 2
(b) –2
(c) –1/2
(d) 1/2
The fraction can be written as F = (4 + c) (2 + c) / (5 + c)
Put 5 + c = t or c = t – 5
∴ F = (t – 3) (t – 1)/t
= (t^2 – rt + 3)/t
= (t^2 – 4t + 4 – 1)/t
= (t – 2)^2/ t – 1/t
Hence, the given expression is minimum, if the square term is equal to zero
∴(t-2)/t = 0 or t = 2
Hence answer is A
