Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 4 - Number Representation and Calculation - 4.1 Our Hindu-Arabic System and Early Positional Systems - Exercise Set 4.1 - Page 219: 77

Answer

Since, the expression \[{{10}^{2}}\text{+ }{{11}^{2}}+{{12}^{2}}\]is written as, \[\begin{align} & {{10}^{2}}\text{ }+\text{ }{{11}^{2}}\text{ }+\text{ }{{12}^{2}}=10\cdot 10+11\cdot 11+12\cdot 12 \\ & =100+121+144 \\ & =365 \end{align}\] …… (1) And, the expression \[{{13}^{2}}\text{ }+\text{ }{{14}^{2}}\]written as, \[\begin{align} & {{13}^{2}}\text{ }+\text{ }{{14}^{2}}=13\cdot 13+14\cdot 14 \\ & =169+196 \\ & =365 \end{align}\] …… (2) From 1 and 2 equations, both the expression are equals also 365 is the number of days in a non-leap year. Hence, both sides of the expression \[{{10}^{2}}\text{ }+\text{ }{{11}^{2}}\text{ }+\text{ }{{12}^{2}}\text{ }=\text{ }{{13}^{2}}\text{ }+\text{ }{{14}^{2}}\]are equal and the significance of the sum is that sum is the number of days in a non-leap year.
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