Question

if a and b are two unequal rational numbers, show that a+b by2 rational number lying between a and b​

Answer 1

Answer:

a+b/2 is the average

Step-by-step explanation:

a+b/2 is the average and therefore has to be between them!!

It is also equal to a-b/2 + b

Answer 2

Given : two number a and b

To show : $\frac{a+b}{2}$rational number lying between a and b​

Step-by-step explanation:

let the two numbers be a and b where a <b

then

$\frac{a+b}{2}-a = \frac{b-a}{2}>0\\\\thus\\\\a<\frac{a+b}{2}\\\\b - \frac{a+b}{2}= \frac{b-a}{2}= \frac{b-a}{2}>0\\\\thus \\\\\frac{a+b}{2}<b\\\\therefore \\\\a<\frac{a+b}{2}<b$

hence ,  $\frac{a+b}{2}$ is the rational number lie between the rational numbers a and b

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