2006-09-27 20:34:28 · 4 answers · asked by Sanjeev s 1 in Science & Mathematics ➔ Mathematics
3^x+4^x=5^x so (3/5)^x+(4/5)^x=1
if x>2 so (3/5)^x< 9/25; (4/5)^x< 16/25 so (3/5)^x+(4/5)^x<1
if x<2 so (3/5)^x> 9/25; (4/5)^x> 16/25 so (3/5)^x+(4/5)^x>1
therefore x=2
2006-09-27 21:37:10 · answer #1 · answered by Manh B 1 · 0⤊ 0⤋
Since Wiles finally proved Fermats' Theorem, you could use that since 2, 4, and 5 are all clearly integers âº
Doug
2006-09-28 03:41:09 · answer #2 · answered by doug_donaghue 7 · 1⤊ 0⤋
Well, you can try using log.
x = log 5(3^x + 4^x)
= log 5(3^x) + log 5(4^x)
2006-09-28 04:04:43 · answer #3 · answered by nayanmange 4 · 0⤊ 1⤋
you know this is pythagorus, right?
well, when they say that a side squared, such as c^2, it is as if a square with side lengths of c was on that hypoteneuse.
Hint: use logarithm functions on each a,b,c
2006-09-28 03:40:13 · answer #4 · answered by Double Century Dude 3 · 0⤊ 1⤋