Question

5^2x+35^x-2*49^x=0
Multumesc

Answer 1

$5^{2x}+35^{x}-2*49 ^{x}=0 \\ \\5^{2x}+(5*7)^{x} - 2* 7^{2x} =0 \\ \\ 5^{2x}+5^{x} *7^{x} -2*7^{2x}=0~~/:5^{2x};~x\ \textgreater \ 0 \\ \\ 1+ (\frac{7}{5})^{x}-2*[ (\frac{7}{5})^{x}]^{2} =0 \\ \\ Notam~( \frac{7}{5})^{x} = t,~~t\ \textgreater \ 0 \\ \\ -2t^{2}+t+1=0 \\ -2t^{2}+2t-t+1=0 \\ 2t(1-t)-(1-t)=0 \\ (1-t)(2t-1)=0 \\ \\ t_{1}=1;~~t_{2}= \frac{1}{2} \\ \\ t=1 \\ (\frac{7}{5})^{x}=1 \\ x=0 \\ \\ t= \frac{1}{2} \\ \\ (\frac{7}{5})^{x}= \frac{1}{2} \\ \\ x= log ~~ \frac{1}{2} \\ ~~~~~~~~~~ \frac{7}{5}$

$Solutiile~sunt: S=(0; ~log ~~\frac{1}{2} )\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \frac{7}{5}$

Poate ii mai trebuie si altcuiva, de aceea tot am zis s-o rezolv.