Răspuns:
[tex]x=\frac{1}{39}[/tex]
Explicație pas cu pas:
[tex]\frac{5}{8} *[\frac{5}{8}+ \frac{5}{8}*( \frac{8}{5x} +\frac{3}{5})] = 25\\ \frac{5}{8}+ \frac{5}{8}*( \frac{8}{5x} +\frac{3}{5}) = 25 *\frac{8}{5}\\ \frac{5}{8}+ \frac{5}{8}*( \frac{8}{5x} +\frac{3}{5}) = 40\\ \frac{5}{8}*( \frac{8}{5x} +\frac{3}{5})= 40- \frac{5}{8}\\ \frac{5}{8}*( \frac{8}{5x} +\frac{3}{5})=\frac{320-5}{8}\\ \frac{5}{8}*( \frac{8}{5x} +\frac{3}{5})=\frac{315}{8}\\ \frac{8}{5x} +\frac{3}{5}= \frac{315}{8}*\frac{8}{5}\\\frac{8}{5x} +\frac{3}{5}=63\\\frac{8}{5x}= 63-\frac{3}{5}\\[/tex]
[tex]\frac{8}{5x}= \frac{315-3}{5}\\\frac{8}{5x}= \frac{312}{5}\\5x= \frac{40}{312} \\x=\frac{40}{312}*\frac{1}{5} \\x= \frac{1}{39}[/tex]
Verificare
[tex]\frac{5}{8} *[\frac{5}{8}+ \frac{5}{8}*( \frac{8}{5x} +\frac{3}{5})] = 25\\\frac{5}{8} *[\frac{5}{8}+ \frac{5}{8}*( \frac{8}{5*\frac{1}{39} } +\frac{3}{5})] = 25\\\frac{5}{8} *[\frac{5}{8}+ \frac{5}{8}*( \frac{8}{\frac{5}{39} } +\frac{3}{5})] = 25\\\frac{5}{8} *[\frac{5}{8}+ \frac{5}{8}*( \frac{8*39}{5} +\frac{3}{5})] = 25\\\frac{5}{8} *[\frac{5}{8}+ \frac{5}{8}*( \frac{312}{5} +\frac{3}{5})] = 25\\\frac{5}{8} *(\frac{5}{8}+ \frac{5}{8}* \frac{315}{5}) = 25\\[/tex]
[tex]\frac{5}{8} *(\frac{5}{8}+ \frac{315}{8}) = 25\\\frac{5}{8} * \frac{320}{8} = 25\\\frac{1600}{64} =25\\25=25[/tex]
