Question

Cum se rezolva 4^x+9^x+16^x=6^x+8^x+12^x?

Answer 1

[tex]Notam : 2^{x}=a, 3^{x}=b, 4^{x}=c, ecuatia. devine: a^{2}+ b^{2} + c^{2} = ab+ac+bc , inmultim cu 2 trecem in stanga si restrangem: (a-b)^{2}+( a-c)^{2}+( b-c)^{2}=0, adevarata. numai.pentru. a=b=c, dar 2^{x} = 3^{x}= 4^{x} solutie. unica. x=0. [/tex]