2

Suppose ${3^x} + {4^x} = {5^x}$.

What is zero of this equation?

BrianO
  • 16,579
DP11
  • 21

1 Answers1

1

$x=2$

Since

${\left( {\frac{3}{5}} \right)^x} + {\left( {\frac{4}{5}} \right)^x} = 1 = {(\sin x)^2} + {(\cos x)^2} \Rightarrow x = 2$

H....
  • 1,879
  • 1
    Very nice (much nicer than stating Pythagoras)!!! – barak manos Nov 08 '15 at 08:24
  • 2
    @barakmanos It's just Pythagoras ($\sin^2 x + \cos^2 x = 1$ is just stating Pythagoras as well). And why does the deduction follow? It's a non-sequitur in my opinion. – Henno Brandsma Nov 08 '15 at 08:28
  • @HennoBrandsma: By "stating Pythagoras", I meant stating the well-known fact that $3^2+4^2=5^2$ (which is what I had in mind when I noted "Pythagoras" in a comment to the question). So I do not agree that stating $\sin^2x+\cos^2x=1$ is an equivalent. I do agree, however, that the OP is probably missing a "$\implies$" here or something to make the deduction clearer. – barak manos Nov 08 '15 at 08:35