Asked: If a, b, and c are not equal to zero, what is the difference between the maximum and minimum value of S?
\(S=1 + \frac{|a|}{a} + \frac{2|b|}{b} + \frac{3|ab|}{ab} −\frac{4|c|}{c}\)
For Smax: -
a>0; b>0; ab>0; c<0
Smax = 1 + 1 + 2 + 3 + 4 = 11
For Smin: -
a>0; b<0; ab<0; c>0
Smin = 1 + 1 - 2 - 3 - 4 = -7
Smax - Smin = 11 - (-7) = 18
IMO C
\(S=1 + \frac{|a|}{a} + \frac{2|b|}{b} + \frac{3|ab|}{ab} −\frac{4|c|}{c}\)
For Smax: -
a>0; b>0; ab>0; c<0
Smax = 1 + 1 + 2 + 3 + 4 = 11
For Smin: -
a>0; b<0; ab<0; c>0
Smin = 1 + 1 - 2 - 3 - 4 = -7
Smax - Smin = 11 - (-7) = 18
IMO C
Statistics : Posted by Kinshook • on 29 Jan 2016, 03:28 • Replies 8 • Views 9225
