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Misalkan d dan f dua bilangan real yang memenuhi Persamaan 2d3−3d−1=0 dan f2+3f−2=0 dengan df=0 nilai dari (df+d+1)f−1 adalah ...

Pertanyaan

Misalkanspace d spacedanspace f spacedua bilangan real yang memenuhi Persamaan 2 d cubed minus 3 d minus 1 equals 0 dan f squared plus 3 f minus 2 equals 0 dengan d f not equal to 0 nilai dari left parenthesis d f plus d plus 1 right parenthesis f to the power of negative 1 end exponent adalah ... 

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 d cubed minus 3 d minus 1 end cell equals 0 row cell open parentheses d plus 1 close parentheses open parentheses 2 d squared minus 2 d minus 1 close parentheses end cell equals 0 row cell open parentheses d plus 1 close parentheses end cell equals 0 row d equals cell negative 1 end cell end table 

atau table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 d squared minus 2 d minus 1 close parentheses 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 0 end table, dengan rumus abc didapatkan

table attributes columnalign right center left columnspacing 0px end attributes row cell d subscript 1 comma 2 end subscript end cell equals cell fraction numerator 2 plus-or-minus square root of 2 squared minus 4 times 2 times negative 1 end root over denominator 2 times 2 end fraction end cell row blank equals cell fraction numerator 2 plus-or-minus square root of 4 plus 8 end root over denominator 4 end fraction end cell row blank equals cell fraction numerator 2 plus-or-minus 2 square root of 3 over denominator 4 end fraction end cell row cell d subscript 1 end cell equals cell fraction numerator 1 plus square root of 3 over denominator 2 end fraction end cell row cell d subscript 2 end cell equals cell fraction numerator 1 minus square root of 3 over denominator 2 end fraction end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell f squared plus 3 f minus 2 end cell equals 0 row f equals cell fraction numerator negative 3 plus-or-minus square root of 3 squared minus 4 times 1 times negative 2 end root over denominator 2 times 1 end fraction end cell row blank equals cell fraction numerator negative 3 plus-or-minus square root of 9 plus 8 end root over denominator 2 end fraction end cell row cell f subscript 1 end cell equals cell fraction numerator negative 3 plus square root of 17 over denominator 2 end fraction end cell row cell f subscript 2 end cell equals cell fraction numerator negative 3 minus square root of 17 over denominator 2 end fraction end cell end table 

Pilih d equals negative 1 dan f equals fraction numerator negative 3 plus square root of 17 over denominator 2 end fraction maka nilai left parenthesis d f plus d plus 1 right parenthesis f to the power of negative 1 end exponent sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis d f plus d plus 1 right parenthesis f to the power of negative 1 end exponent end cell equals cell open square brackets negative 1 times open parentheses fraction numerator negative 3 plus square root of 17 over denominator 2 end fraction close parentheses plus open parentheses negative 1 close parentheses plus 1 close square brackets fraction numerator 2 over denominator negative 3 plus square root of 17 end fraction end cell row blank equals cell fraction numerator 3 minus square root of 17 over denominator up diagonal strike 2 end fraction times fraction numerator up diagonal strike 2 over denominator negative 3 plus square root of 17 end fraction end cell row blank equals cell fraction numerator 3 minus square root of 17 over denominator negative 3 plus square root of 17 end fraction end cell row blank equals cell fraction numerator up diagonal strike 3 minus square root of 17 end strike over denominator negative up diagonal strike open parentheses 3 minus square root of 17 close parentheses end strike end fraction end cell row blank equals cell negative 1 end cell end table 

Jadi, nilai left parenthesis d f plus d plus 1 right parenthesis f to the power of negative 1 end exponent adalah negative 1 

 

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