Functions (XII)

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Question

$if a,b,c are non-zero rational numbers then the sum of all the possible values of \frac{|a|}{a} + \frac{|b|}{b} + \frac{|c|}{c}$

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Solution

$Let x= \frac{|a|}{a} + \frac{|b|}{b} + \frac{|c|}{c} I f e x a c t l y o n e i s n e g a t i v e t h e n x = 1, i f t w o a r e n e g a t i v e t h e n x = - 1$
$i f a l l t h r e e a r e n e g a t i v e x = - 3, i f a l l t h r e e a r e p o s i t i v e t h e n x = 3 T h e n t h e r e q u i r e d s u m i s 0$

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Functions (XII)

Remember concepts with our Masterclasses.

if a,b,c are non-zero rational numbers then the sum of all the possible values of aa+bb+cc

Let x=aa+bb+cc If exactly one is negative then x=1, if two are negative then x=-1 if all three are negative x=-3, if all three are positive then x=3 Then the required sum is 0

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$if a,b,c are non-zero rational numbers then the sum of all the possible values of \frac{|a|}{a} + \frac{|b|}{b} + \frac{|c|}{c}$