tex]...

April 2021 1 16 Report

упростите выражение
а) ([tex] (a^{ \frac{1}{6} } + 1) ( a^{ \frac{1}{6} } -1) ( a^{ \frac{1}{3} } +1)
[/tex]
б) ([tex] (\frac{ a-b }{ a^{ \frac{1}{2} } - b^{ \frac{1}{2} } } - \frac{ a^{ \frac{3}{2} }- b^{ \frac{3}{2} } }{a-b}) * ( b^{ \frac{1}{2} } + a^{ \frac{1}{2} } ) [/tex]

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Artem112

Verified answer

$(a^{ \frac{1}{6} } + 1) ( a^{ \frac{1}{6} } -1) ( a^{ \frac{1}{3} } +1)= (a^{ \frac{1}{3} } -1) ( a^{ \frac{1}{3} } +1)=a^{ \frac{2}{3} } -1$

$(\frac{a-b}{a^{\frac{1}{2}}-b^{\frac{1}{2}}}-\frac{a^{\frac{3}{2}}-b^{ \frac{3}{2}}}{a-b})(b^{\frac{1}{2}}+a^{\frac{1}{2}})=
(\frac{(a-b)(a^{\frac{1}{2}}+b^{\frac{1}{2}})}{a-b}- \frac{a^{\frac{3}{2}}-b^{\frac{3}{2}}}{a-b})(b^{\frac{1}{2}}+a^{\frac{1}{2}})=$
$=(\frac{a^{\frac{3}{2}}+ab^{\frac{1}{2}}-ba^{\frac{1}{2}}-b^{\frac{3}{2}}-a^{\frac{3}{2}}+b^{\frac{3}{2}}}{a-b})(b^{\frac{1}{2}}+a^{ \frac{1}{2}})=
(\frac{a^{\frac{1}{2}}b^{\frac{1}{2}}(a^{\frac{1}{2}}-b^{\frac{1}{2}})}{a-b})(b^{\frac{1}{2}}+a^{ \frac{1}{2}})=
\\\
=\frac{a^{\frac{1}{2}}b^{\frac{1}{2}}(a-b)}{a-b}=a^{\frac{1}{2}}b^{\frac{1}{2}$

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