Determine if the statement is true or false.For all real numbers a and b, if a < b then a < frac{a + b}{2} < b.

Emeli Hagan 2021-01-06 Answered

Determine if the statement is true or false.
For all real numbers a and b, if a < b then a < a + b2 < b.

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Expert Answer

gotovub
Answered 2021-01-07 Author has 98 answers

Let assume that a and b are real numbers such that a < b.
Now using b > a,
a + b2 > a + b2
> 2a2
> a
And using a < b,
a + b2 < b + b2
< 2b2
< b
This implies,
a < a + b2 < b
Therefore, the ststement is true.

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