[tex]4^x + 9^x + 25^x = 6^x + 10^x + 15^x [/tex]
[tex](2^x)^2 + (3^x)^2 + (5^x)^2 = 2^x*3^x + 3^x*5^x+2^x*5^x[/tex]
[tex]2^x = a; 3^x =b; 5^x = c[/tex]
[tex]a^2 + b^2 + c^2 = ab+bc+ca | *2[/tex]
[tex]2a^2 + 2b^2 +2c^2 -2ab-2bc-2ac=0[/tex]
[tex](a-b)^2+(b-c)^2+(a-c)^2=0 [/tex]
De aici rezulta ca
[tex]a=b=c =\ \textgreater \ 2^x=3^x=5^x [/tex]; x=0 solutie unica
