Difference between revisions of "2011 UNCO Math Contest II Problems/Problem 8"
(→Solution) |
(→Solution) |
||
| Line 14: | Line 14: | ||
== Solution == | == Solution == | ||
(a) By testing the perfect squares up to <math>74</math>, you can see that <math>\boxed{74=25+49=5^2+7^2}</math>. | (a) By testing the perfect squares up to <math>74</math>, you can see that <math>\boxed{74=25+49=5^2+7^2}</math>. | ||
| + | \begin{align*} | ||
| + | \text{ } | ||
| + | \end{align*} | ||
(b) <math>45 \cdot 74 = 9^2 + 57^2 = 27^2 + 51^2</math>. | (b) <math>45 \cdot 74 = 9^2 + 57^2 = 27^2 + 51^2</math>. | ||
== See Also == | == See Also == | ||
{{UNCO Math Contest box|n=II|year=2011|num-b=7|num-a=9}} | {{UNCO Math Contest box|n=II|year=2011|num-b=7|num-a=9}} | ||
Latest revision as of 12:54, 2 May 2024
Problem
The integer 
can be expressed as a sum of two squares as 
.
(a) Express 
as the sum of two squares.
(b) Express the product 
as the sum of two squares.
(c) Prove that the product of two sums of two squares, 
, can be represented
as the sum of two squares.
Solution
(a) By testing the perfect squares up to , you can see that 
.
\begin{align*}
\text{ }
\end{align*}
(b) 
.
See Also
| 2011 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
