Concept explainers
Whether the given statement is true for all real numbers.
Answer to Problem 33WE
If a number is between 0 and 1 and if it is multiplied by itself, the result will be smaller than the original number.
Explanation of Solution
Given:
The given statement is:
Calculation:
From the first two given inequalities, it can be said that a is a real number that lies between 0 and 1.
According to the third inequality, the square of a is less than a.
Square of a number is equal to the product of the number with itself.
Let us take an example:
Let a be a number between 0 and 1, say 0.5.
Therefore, it is proven that if a number is between 0 and 1 and if it is multiplied by itself, the result will be smaller than the original number.
Chapter 2 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
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