Pertanyaan

2. Tentukan nilai ( ( y x ) 2 − 1 ) − 2 1 ( ( x y ) 2 + 1 ) − 2 1 ( 1 + ( y x ) 2 ) − 2 1 ( 1 − ( x y ) 2 ) − 2 1 .

2. Tentukan nilai $\frac{( 1 + ( \frac{x}{y} ) ^{2} ) ^{- \frac{1}{2}} ( 1 - ( \frac{y}{x} ) ^{2} ) ^{- \frac{1}{2}}}{( ( \frac{x}{y} ) ^{2} - 1 ) ^{- \frac{1}{2}} ( ( \frac{y}{x} ) ^{2} + 1 ) ^{- \frac{1}{2}}}$ .

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Habis dalam

Klaim

P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Jawaban

nilaidari .

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

Untuk soal persamaan eksponen tersebut berlaku sifat-sifat berikut: Dengan demikian, nilaidari .

Untuk soal persamaan eksponen tersebut berlaku sifat-sifat berikut:

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