Question

Допоможіть будь ласка!!!​

Answer 1

$\displaystyle\bf\\1)\\\\\frac{a^{\frac{5}{6} } +a^{\frac{1}{3} } }{a^{\frac{5}{6} } -a^{\frac{1}{3} } } =\frac{a^{\frac{5}{6} } +a^{\frac{2}{6} } }{a^{\frac{5}{6} } -a^{\frac{2}{6} } } =\frac{a^{\frac{2}{6} } \cdot(a^{\frac{3}{6} }+1) }{a^{\frac{2}{6} } \cdot(a^{\frac{3}{6} } -1)} =\frac{a^{\frac{1}{2} } +1}{a^{\frac{1}{2} } -1}=\frac{\sqrt{a} +1}{\sqrt{a} -1} \\\\\\a=1,44\\\\\\\frac{\sqrt{a} +1}{\sqrt{a} -1} =\frac{\sqrt{1,44} +1}{\sqrt{1,44} -1} =\frac{1,2+1}{1,2-1} =\frac{2,2}{0,2} =11$

$\displaystyle\bf\\2)\\\\\frac{2x^{\frac{1}{2} } }{x-4} -\frac{1}{x^{\frac{1}{2} }-2 }= \frac{2x^{\frac{1}{2} } }{(x^{\frac{1}{2} })^{2} -2^{2} } -\frac{1}{x^{\frac{1}{2} }-2 }= \frac{2x^{\frac{1}{2} } }{(x^{\frac{1}{2} } -2)(x^{\frac{1}{2} } +2)} -\frac{1}{x^{\frac{1}{2} }-2 }= \\\\\\=\frac{2x^{\frac{1}{2} } -x^{\frac{1}{2} } -2}{(x^{\frac{1}{2} }-2)(x^{\frac{1}{2} } +2) } =\frac{x^{\frac{1}{2} } -2}{(x^{\frac{1}{2} }-2)(x^{\frac{1}{2} } +2) } =\frac{1}{x^{\frac{1}{2} } +2} =\frac{1}{\sqrt{x} +2}$

$\displaystyle\bf\\x=9\\\\\\\frac{1}{\sqrt{x} +2} =\frac{1}{\sqrt{9} +2}=\frac{1}{3+2} =\frac{1}{5} =0,2$