Difference between revisions of "2011 UNCO Math Contest II Problems/Problem 8"

(Solution)
(Solution)
Line 13: Line 13:
  
 
== Solution ==
 
== Solution ==
(a) <math>74</math> (b) <math>45 \times 74</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>}$.
  
 
== 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}}

Revision as of 21:50, 1 March 2019

Problem

The integer $45$ can be expressed as a sum of two squares as $45 = 3^2 + 6^2$.

(a) Express $74$ as the sum of two squares.

(b) Express the product $45\cdot 74$ as the sum of two squares.

(c) Prove that the product of two sums of two squares, $(a^2+b^2)(c^2+d^2)$ , can be represented as the sum of two squares.


Solution

(a) By testing the perfect squares up to $74$, you can see that $\boxed{74=25+49=5^2+7^2$ (Error compiling LaTeX. Unknown error_msg)}$.

See Also

2011 UNCO Math Contest II (ProblemsAnswer KeyResources)
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