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

Revision as of 20:50, 1 March 2019

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.

(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)}$.

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 == 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 ==
 {{UNCO Math Contest box|n=II|year=2011|num-b=7|num-a=9}}

2011 UNCO Math Contest II (Problems • Answer Key • Resources)
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