Question

verify that {a+b} is either less than or equal to {a}+{b} for the following values of a and b

Answer 1

Given: The correct question is: Verify that | a+b | is either less than or equal to |a|+|b| for the following values of a and b.

To find: (1) a = 7/3, b = 2/3  (2) a = -3/2, b = 3/4

Solution:

• Now we have given to prove  | a+b | = |a|+|b|

• We have (1) a = 7/3, b = 2/3  (2) a = -3/2, b = 3/4

• (1) a = 7/3, b = 2/3

                 | a+b | = | 7/3 + 2/3 | = |9/3| = |3| = 3

                 |a|+|b| = |7/3| + |2/3| = 7/3 + 2/3 = 3

                 So in this case  | a+b | = |a| + |b|

• (2) a = -3/2, b = 3/4

                 | a+b | = | -3/2 + 3/4 | = |-12 + 6 / 8| = |-6/8| = 6/8 = 3/4

                 |a|+|b| = |-3/2| + |3/4| = 3/2 + 3/4 = 12 + 6 / 8 = 18/8 = 9/4

                 So in this case  | a+b | ≠ |a| + |b|

Answer:

              So in first case only | a+b | = |a| + |b|.