RE: Test Your Math Skills and Win SBD # 2

1. x^2 < x^4
   Let x = -1
   (-1)^2 < (-1)^4
   1 < 1 , FALSE
   Let x= -2
   (-2)^2 < (-2)^4
   4 < 16 , TRUE
   Let x = -3
   (-3)^2 < (-3)^4
   9 < 81 , TRUE
   Therefore, the inequality is FALSE for all values of x.

2. x^3 < x^4
   Let x= -1
   (-1)^3 < (-1)^4
   -1 < 1, TRUE
   Let x= -2
   (-2)^3 < (-2)^4
   -8 < 4 , TRUE
   Let x= -3
   (-3)^3 < (-3)^4
   -27 < 9, TRUE
   Therefore, the inequality is TRUE for all values of x.

3. x + (1/x) < 0
   Let x= -1
   (-1) + (1/(-1)) < 0
   -1 - 1 < 0
   -2 < 0 , TRUE
   Let x= -2
   (-2) + (1/(-2)) < 0
   -2 - (1/2) < 0
   -(5/2) < 0, TRUE
   Let x= -3
   (-3)+ (1/(-3)) < 0
   -3 - (1/3) < 0
   -(10/3), TRUE
   Therefore the inequality is TRUE for all values of x.

4. x = √ x^2
   Let x= -1
   (-1) = √(-1)^2
   -1 = -1, TRUE
   Let x = -2
   (-2) = √(-2)^2
   -2 = -2, TRUE
   Let x= -3
   (-3) = √(-3)^2
   -3 = -3, TRUE
   Therefore the inequality is TRUE for all values of x.

To summarize, The inequalities of #2, #3, and #4 are TRUE except #1 which is FALSE.