Răspuns:
a) [tex]\sqrt{\frac{625}{81} } :\sqrt{\frac{25}{9}}+3\frac{1}{3} :\sqrt{1,(7)} -\sqrt{36} :\sqrt{6^{4}} =\\=\frac{25}{9} :\frac{5}{3}+\frac{10}{3} :\sqrt{\frac{16}{9}} -6:6^{2} =\\=\frac{25}{9} *\frac{3}{5}+\frac{10}{3} :\frac{4}{3} -\frac{6}{6^{2}} =\\=\frac{5}{3}+\frac{10}{3} *\frac{3}{4} -\frac{1}{6} =\frac{2)5}{3}+\frac{3)5}{2}-\frac{1}{6} = \frac{10+15-1}{6} =\frac{24}{6} =4[/tex]
b) [tex]x=\sqrt{\frac{74}{71}[(\frac{1}{1*2}+\frac{1}{2*3}+...+\frac{1}{36*37})-(\frac{1}{37*38}+\frac{1}{38*39}+...+\frac{1}{73*74})]}[/tex]
[tex]\frac{1}{n}-\frac{1}{n+1} =\frac{1}{n(n+1)}[/tex]
[tex]x=\sqrt{\frac{74}{71}[(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+ ...+\frac{1}{36}-\frac{1}{37} )-(\frac{1}{37}-\frac{1}{38}+\frac{1}{38}-\frac{1}{39}+...+\frac{1}{73}-\frac{1}{74})] }[/tex]
[tex]x=\sqrt{\frac{74}{71}[(1-\frac{1}{37})-(\frac{1}{37}-\frac{1}{74})]}[/tex]
[tex]x=\sqrt{\frac{74}{71}(1-\frac{1}{37}+\frac{1}{37}+\frac{1}{74})}[/tex]
[tex]x=\sqrt{\frac{74}{71}(1+\frac{1}{74})}[/tex]
[tex]x=\sqrt{\frac{74}{71}*\frac{75}{74}}[/tex]
[tex]x=\sqrt{\frac{75}{71} }[/tex]
Explicație pas cu pas:
