for the rational numbers between
a and b the number that always lies between a and b is
Answers
Given : two rational number a & b and 4 options 2a , 2 b , (a + b)/2 , (a - b)/2
To find : which of given option always lies between a and b is
Solution:
Let check each case considering a < b
a < 2a < b
subtracting a from both sides
=> 0 < a < b - a
=> a has to be greater than 0 for 2a to be between
a < 2b < b
Subtracting b from both sides
=> a - b < b < 0
=> b has to be less than 0 for 2b to be between a & b
a < (a - b)/2 < b
2a < a - b < 2b
subtracting a from both sides
a < - b < 2b - a
a < b , hence a < - b not possible
a < (a + b)/2 < b
=> 2a < a + b < 2b
2a < a + b & subtracting a from both sides
=> a < b
a + b < 2b & subtracting b from both sides
=> a < b
Hence satisfied
So (a + b)/2 always lies between rational number a & b
Learn More:
Insert 4 rational numbers between 3/4 and 1 without using a+b/2 ...
https://brainly.in/question/7747173
Answer: THIS IS
YOUR ANSWER
Explanation:
[a+b] upon 2