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2. Tentukan nilai ((yx​)2−1)−21​((xy​)2+1)−21​(1+(yx​)2)−21​(1−(xy​)2)−21​​.

Pertanyaan

2. Tentukan nilai fraction numerator open parentheses 1 plus open parentheses begin display style x over y end style close parentheses squared close parentheses to the power of negative begin display style 1 half end style end exponent open parentheses 1 minus open parentheses begin display style y over x end style close parentheses squared close parentheses to the power of negative begin display style 1 half end style end exponent over denominator open parentheses open parentheses begin display style x over y end style close parentheses squared minus 1 close parentheses to the power of negative begin display style 1 half end style end exponent open parentheses open parentheses begin display style y over x end style close parentheses squared plus 1 close parentheses to the power of negative begin display style 1 half end style end exponent end fraction.

Pembahasan Soal:

Untuk soal persamaan eksponen tersebut berlaku sifat-sifat berikut:

  • open parentheses a over b close parentheses to the power of p equals a to the power of p over b to the power of p space dengan space b not equal to 0 
  • a to the power of negative p end exponent equals 1 over a to the power of p space dengan space a not equal to 0 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator open parentheses 1 plus open parentheses begin display style x over y end style close parentheses squared close parentheses to the power of negative begin display style 1 half end style end exponent open parentheses 1 minus open parentheses begin display style y over x end style close parentheses squared close parentheses to the power of negative begin display style 1 half end style end exponent over denominator open parentheses open parentheses begin display style x over y end style close parentheses squared minus 1 close parentheses to the power of negative begin display style 1 half end style end exponent open parentheses open parentheses begin display style y over x end style close parentheses squared plus 1 close parentheses to the power of negative begin display style 1 half end style end exponent end fraction end cell equals cell fraction numerator open parentheses 1 plus begin display style x squared over y squared end style close parentheses to the power of negative begin display style 1 half end style end exponent open parentheses 1 minus begin display style y squared over x squared end style close parentheses to the power of negative begin display style 1 half end style end exponent over denominator open parentheses begin display style x squared over y squared minus 1 end style close parentheses to the power of negative begin display style 1 half end style end exponent open parentheses begin display style y squared over x squared plus 1 end style close parentheses to the power of negative begin display style 1 half end style end exponent end fraction end cell row blank equals cell fraction numerator open parentheses begin display style fraction numerator y squared plus x squared over denominator y squared end fraction end style close parentheses to the power of negative begin display style 1 half end style end exponent open parentheses begin display style fraction numerator x squared minus y squared over denominator x squared end fraction end style close parentheses to the power of negative begin display style 1 half end style end exponent over denominator open parentheses begin display style fraction numerator x squared minus y squared over denominator y squared end fraction end style close parentheses to the power of negative begin display style 1 half end style end exponent open parentheses begin display style fraction numerator y squared plus x squared over denominator x squared end fraction end style close parentheses to the power of negative begin display style 1 half end style end exponent end fraction end cell row blank equals cell fraction numerator begin display style 1 over open parentheses begin display style fraction numerator y squared plus x squared over denominator y squared end fraction end style close parentheses to the power of begin display style 1 half end style end exponent 1 over open parentheses begin display style fraction numerator x squared minus y squared over denominator x squared end fraction end style close parentheses to the power of begin display style 1 half end style end exponent end style over denominator begin display style 1 over open parentheses begin display style fraction numerator x squared minus y squared over denominator y squared end fraction end style close parentheses to the power of begin display style 1 half end style end exponent 1 over open parentheses begin display style fraction numerator y squared plus x squared over denominator x squared end fraction end style close parentheses to the power of begin display style 1 half end style end exponent end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 1 over denominator square root of begin display style fraction numerator y squared plus x squared over denominator y squared end fraction end style end root end fraction fraction numerator 1 over denominator square root of begin display style fraction numerator x squared minus y squared over denominator x squared end fraction end style end root end fraction end style over denominator begin display style fraction numerator 1 over denominator square root of begin display style fraction numerator x squared minus y squared over denominator y squared end fraction end style end root end fraction fraction numerator 1 over denominator square root of begin display style fraction numerator y squared plus x squared over denominator x squared end fraction end style end root end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 1 over denominator up diagonal strike begin display style 1 over y end style end strike square root of y squared plus x squared end root end fraction fraction numerator 1 over denominator up diagonal strike begin display style 1 over x end style end strike square root of x squared minus y squared end root end fraction end style over denominator begin display style fraction numerator 1 over denominator up diagonal strike begin display style 1 over y end style end strike square root of x squared minus y squared end root end fraction fraction numerator 1 over denominator up diagonal strike begin display style 1 over x end style end strike square root of y squared plus x squared end root end fraction end style end fraction end cell row blank equals cell fraction numerator square root of x squared minus y squared end root square root of y squared plus x squared end root over denominator square root of y squared plus x squared end root square root of x squared minus y squared end root end fraction end cell row blank equals 1 end table 

Dengan demikian, nilai dari begin mathsize 12px style fraction numerator open parentheses 1 plus open parentheses begin display style x over y end style close parentheses squared close parentheses to the power of negative begin display style 1 half end style end exponent open parentheses 1 minus open parentheses begin display style y over x end style close parentheses squared close parentheses to the power of negative begin display style 1 half end style end exponent over denominator open parentheses open parentheses begin display style x over y end style close parentheses squared minus 1 close parentheses to the power of negative begin display style 1 half end style end exponent open parentheses open parentheses begin display style y over x end style close parentheses squared plus 1 close parentheses to the power of negative begin display style 1 half end style end exponent end fraction equals 1 end style.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

P. Tessalonika

Mahasiswa/Alumni Universitas Negeri Medan

Terakhir diupdate 06 Oktober 2021

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