document.write( "Question 1209213: If $\"ab%5E2c%5E4=2430000\"$ , where a, b and c are distinct positive integers greater than 1, What is the greatest possible value of a+b+c?
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Algebra.Com's Answer #847853 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Tutor @ikleyn has pointed out that I lost track of what I was doing in my original response. Following is my corrected solution.

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\n" ); document.write( "In the given algebraic expression, the exponent on a is odd and the exponents on b and c are even; in the factored form of the constant, the exponent on the factor 3 is odd and the exponents on the factors 2 and 5 are even. That means a must be 3^5=243.

\n" ); document.write( "That leaves us with

\n" ); document.write( " $\"%28b%5E2%29%28c%5E4%29=%282%5E4%29%285%5E4%29\"$

\n" ); document.write( "Since a, b, and c are each greater than 1, there are two possibilities:
\n" ); document.write( "(1) $\"b%5E2=2%5E4\"$ and $\"c%5E4=5%5E4\"$ , which gives us $\"b=2%5E2=4\"$ and $\"c=5\"$
\n" ); document.write( "(2) $\"b%5E2=5%5E4\"$ and $\"c%5E4=2%5E4\"$ , which gives us $\"b=5%5E2=25\"$ and $\"c=2\"$

\n" ); document.write( "For case (1), a+b+c = 243+4+5 = 252; for case (2), a+b+c = 243+25+2 = 270.

\n" ); document.write( "ANSWER: 270

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