Bài tập 19 trang 82 SGK Toán 12 NC

Bài tập 19 trang 82 SGK Toán 12 NC

a)

\(\begin{array}{l}
{a^{ - 2\sqrt 2 }}{\left( {\frac{1}{{{a^{ - \sqrt 2  - 1}}}}} \right)^{\sqrt 2  + 1}}\\
 = {a^{ - 2\sqrt 2 }}{\left( {{a^{\sqrt 2  + 1}}} \right)^{\sqrt 2  + 1}}\\
 = {a^{ - 2\sqrt 2 }}.{a^{3 + 2\sqrt 3 }} = {a^3}
\end{array}\)

b)

\(\begin{array}{l}
{\left( {\frac{{{a^{\sqrt 3 }}}}{{{b^{\sqrt 3  - 1}}}}} \right)^{\sqrt 3  + 1}}\frac{{{a^{ - 1 - \sqrt 3 }}}}{{{b^{ - 2}}}}\\
 = \frac{{{a^{3 + \sqrt 3 }}}}{{{b^2}}}.\frac{{{a^{ - 1 - \sqrt 3 }}}}{{{b^{ - 2}}}} = {a^2}
\end{array}\)

c)

\(\begin{array}{*{20}{l}}
\begin{array}{l}
\frac{{{a^{2\sqrt 2 }} - {b^{2\sqrt 3 }}}}{{{{\left( {{a^{\sqrt 2 }} - {b^{\sqrt 3 }}} \right)}^2}}} + 1\\
 = \frac{{{a^{2\sqrt 2 }} - {b^{2\sqrt 3 }} + {{\left( {{a^{\sqrt 2 }} - {b^{\sqrt 3 }}} \right)}^2}}}{{{{\left( {{a^{\sqrt 2 }} - {b^{\sqrt 3 }}} \right)}^2}}}
\end{array}\\
\begin{array}{l}
 = \frac{{2{a^{2\sqrt 2 }} - 2{a^{\sqrt 2 }}{b^{\sqrt 3 }}}}{{{{\left( {{a^{\sqrt 2 }} - {b^{\sqrt 3 }}} \right)}^2}}}\\
 = \frac{{2{a^{\sqrt 2 }}\left( {{a^{\sqrt 2 }} - {b^{\sqrt 3 }}} \right)}}{{{{\left( {{a^{\sqrt 2 }} - {b^{\sqrt 3 }}} \right)}^2}}} = \frac{{2{a^{\sqrt 2 }}}}{{{a^{\sqrt 2 }} - {b^{\sqrt 3 }}}}
\end{array}
\end{array}\)

d)

\(\begin{array}{*{20}{l}}
\begin{array}{l}
\sqrt {{{({x^\pi } + {y^\pi })}^2} - {{({4^{\frac{1}{\pi }}}xy)}^\pi }} \\
 = \sqrt {({x^{2\pi }} + {y^{2\pi }} - 2x{y^\pi }} 
\end{array}\\
{ = \sqrt {{{({x^\pi } - {y^\pi })}^2}}  = |{x^\pi } - {y^\pi }|}
\end{array}\)

-- Mod Toán 12