SOLUTION: how would I solve for x?: {{{ 3^x + 4^x = 5^x }}} I know the answer is 2 because of the Pythagorean theorem however I want to know how to solve it algebraically.

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Question 763314: how would I solve for x?: +3%5Ex+%2B+4%5Ex+=+5%5Ex+
I know the answer is 2 because of the Pythagorean theorem however I want to know how to solve it algebraically.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

+3%5Ex+%2B+4%5Ex+=+5%5Ex+ => x=2
recall a right triangle where the sides are in the ratio of the integers 3:4:5
This is one example of the many "Pythagorean triples".

+3%5E2+%2B+4%5E2+=+5%5E2+
+9+%2B+16+=+25+
+25+=+25+