For any a and b that satisfy |a – b| = b – a and a > 0, then |a + 2| + |-b| + |b – a| + |ab| =
Select: A) -ab + 3 B) ab + 2b + 2 C) ab + 2b – 2a – 3 D) -ab + 2b + 3 E) ab + 3
Observation-1: |a – b| = b – a   which is possible only when signs of a and b are Same   Since Given a &gt; 0   so we figure out that a and b are both positive   Observation-2: |a – b| must be Non-Negative and so should be the value of b-a which is possible only when absolute value of b is greater than or equal to absolute value of a   Now you may choose the values of a and b based on above observations   e.g. b = 2 and a=1 and check the value of given functions and options   |a + 2| + |-b| + |b – a| + |ab| = |1 + 2| + |-2| + |2 – 1| + |1*2| = 8   -ab + 3 = -1*2+3= 
<gadget id="calculator">-1*2+3</gadget>
<output>1</output>
1   ab + 2b + 2= 1*2+4+2= 
<gadget id="calculator">1*2+4+2</gadget>
<output>8</output>
8   ab + 2b – 2a – 3=1*2+2*2-2*1-3= 
<gadget id="calculator">1*2+2*2-2*1-3</gadget>
<output>1</output>
1   -ab + 2b + 3=5   ab + 3+ 2  + 3= 
<gadget id="calculator">+ 2  + 3</gadget>
<output>5</output>
5   ab + 3=5   Answer : ab + 2b + 2
<result>B</result>
For any a and b that satisfy |a – b| = b – a and a > 0, then |a + 2| + |-b| + |b – a| + |ab| =