SOLUTION: If {{{3^x+4^x = 5^x}}} Find x. NB:x is 2 but I need the method, thanks

Algebra ->  Exponents -> SOLUTION: If {{{3^x+4^x = 5^x}}} Find x. NB:x is 2 but I need the method, thanks      Log On


   

Question 939954: If 3%5Ex%2B4%5Ex+=+5%5Ex Find x. NB:x is 2 but I need the method, thanks
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

recall the Pythagorean formula
a%5E2%2Bb%5E2+=+c%5E2
you have 3%5Ex%2B4%5Ex+=+5%5Ex, means a=3,b=4, and c=5 which are sides of the Right-Angled Triangle; so, x must be 2
answer: x=2, from the Pythagorean formula for the Right-Angled Triangle