abs max feature implementation

DIRECTORY.md

@@ -66,6 +66,7 @@
   * [Fibonacci](https://github.com/TheAlgorithms/Ruby/blob/master/dynamic_programming/fibonacci.rb)
 
 ## Maths
+  * [Abs Max](https://github.com/TheAlgorithms/Ruby/blob/master/maths/abs_max.rb)
   * [Abs](https://github.com/TheAlgorithms/Ruby/blob/master/maths/abs.rb)
   * [Abs Test](https://github.com/TheAlgorithms/Ruby/blob/master/maths/abs_test.rb)
   * [Add](https://github.com/TheAlgorithms/Ruby/blob/master/maths/add.rb)

maths/abs_max.rb

@@ -0,0 +1,30 @@
+# A ruby program to find absolute maximum
+# Mathematical representation of abs max = ((a + b + absoulte(a - b)) / 2)
+
+def abs_max(x, y)
+  num = x - y
+  max_value = ((x + y + num.abs()) / 2)
+  "The Abs Max of #{x} and #{y} is #{max_value}."
+  rescue
+    "Error: Provide number only!"
+end
+
+# Valid inputs
+puts abs_max(10, 20)
+# The Abs Max of 10 and 20 is 20.
+
+puts abs_max(-10, -1)
+# The Abs Max of -10 and -1 is -1.
+
+puts abs_max(9, -121)
+# The Abs Max of 9 and -121 is 9.
+
+# Invalid inputs
+puts abs_max(2, "-1")
+# Error: Provide number only!
+
+puts abs_max("3", "5")
+# Error: Provide number only!
+
+puts abs_max("a", "5")
+# Error: Provide number only!