Pertanyaan

Sederhanakanlah ( 1 − a ) − 2 1 − ( 1 − a ) 2 1 ( 1 − a ) 2 1 .

Sederhanakanlah $\frac{( 1 - a ) ^{\frac{1}{2}}}{( 1 - a ) ^{- \frac{1}{2}} - ( 1 - a ) ^{\frac{1}{2}}}$ .

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

diperoleh .

diperoleh $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator open parentheses 1 minus a close parentheses to the power of begin display style 1 half end style end exponent over denominator open parentheses 1 minus a close parentheses to the power of negative begin display style 1 half end style end exponent minus open parentheses 1 minus a close parentheses to the power of begin display style 1 half end style end exponent end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 minus a over denominator a end fraction end cell end table$ .

Pembahasan

Jika diberikan suatu bilangan riil dan bilangan rasional maka berlaku sifat-sifat berikut. Misalkan ,sehingga dapat disederhanakan bentuk berikut. Dengan demikian diperoleh .

Jika diberikan suatu bilangan riil dan bilangan rasional m space dan space n maka berlaku sifat-sifat berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell p to the power of m times p to the power of n end cell equals cell p to the power of m plus n end exponent end cell row cell p to the power of negative m end exponent end cell equals cell 1 over p to the power of m end cell end table

Misalkan p equals 1 minus a , sehingga dapat disederhanakan bentuk berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator open parentheses 1 minus a close parentheses to the power of begin display style 1 half end style end exponent over denominator open parentheses 1 minus a close parentheses to the power of negative begin display style 1 half end style end exponent minus open parentheses 1 minus a close parentheses to the power of begin display style 1 half end style end exponent end fraction end cell equals cell fraction numerator p to the power of begin display style 1 half end style end exponent over denominator p to the power of negative begin display style 1 half end style end exponent minus p to the power of begin display style 1 half end style end exponent end fraction end cell row blank equals cell fraction numerator p to the power of begin display style 1 half end style end exponent over denominator begin display style 1 over p to the power of begin display style 1 half end style end exponent minus p to the power of 1 half end exponent end style end fraction end cell row blank equals cell fraction numerator p to the power of begin display style 1 half end style end exponent over denominator begin display style fraction numerator 1 minus p to the power of begin display style 1 half end style end exponent times p to the power of begin display style 1 half end style end exponent over denominator p to the power of begin display style 1 half end style end exponent end fraction end style end fraction end cell row blank equals cell fraction numerator p to the power of begin display style 1 half end style end exponent over denominator begin display style fraction numerator 1 minus p to the power of begin display style 1 half plus 1 half end style end exponent over denominator p to the power of begin display style 1 half end style end exponent end fraction end style end fraction end cell row blank equals cell fraction numerator p to the power of begin display style 1 half end style end exponent over denominator begin display style fraction numerator 1 minus p over denominator p to the power of begin display style 1 half end style end exponent end fraction end style end fraction end cell row blank equals cell p to the power of 1 half end exponent times fraction numerator p to the power of begin display style 1 half end style end exponent over denominator 1 minus p end fraction end cell row blank equals cell fraction numerator p to the power of begin display style 1 half plus 1 half end style end exponent over denominator 1 minus p end fraction end cell row blank equals cell fraction numerator p over denominator 1 minus p end fraction end cell row blank equals cell fraction numerator 1 minus a over denominator 1 minus open parentheses 1 minus a close parentheses end fraction end cell row blank equals cell fraction numerator 1 minus a over denominator a end fraction end cell end table$

Dengan demikian diperoleh $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator open parentheses 1 minus a close parentheses to the power of begin display style 1 half end style end exponent over denominator open parentheses 1 minus a close parentheses to the power of negative begin display style 1 half end style end exponent minus open parentheses 1 minus a close parentheses to the power of begin display style 1 half end style end exponent end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 minus a over denominator a end fraction end cell end table$ .

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