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Pada persamaan 2 x 2 − 4 x − 6 = 0 , tentukan nilai akar-akar berikut! x 1 2 ​ 1 ​ + x 2 2 ​ 1 ​

Pada persamaan , tentukan nilai akar-akar berikut!

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N. Puspita

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nilai .

nilai 1 over x subscript 1 squared plus 1 over x subscript 2 squared equals 10 over 9.

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Apabila persamaan kuadrat mempunyai penyelesaian dan , makanilai: Dan Maka, dari persamaan kuadrat yang mempunyainilai , , dan , diperoleh: Dan Sehingga diperoleh: Ingat bahwa , sehingga: Jadi, nilai .

Apabila persamaan kuadrat straight a x squared plus straight b x plus straight c equals 0 mempunyai penyelesaian x subscript 1 dan x subscript 2, maka nilai:


x subscript 1 plus x subscript 2 equals negative straight b over straight a


Dan


x subscript 1 cross times x subscript 2 equals straight c over straight a


Maka, dari persamaan kuadrat 2 x squared minus 4 x minus 6 equals 0 yang mempunyai nilai straight a equals 2straight b equals negative 4, dan straight c equals negative 6, diperoleh:


table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 plus x subscript 2 end cell equals cell negative straight b over straight a end cell row blank equals cell negative fraction numerator left parenthesis negative 4 right parenthesis over denominator 2 end fraction end cell row blank equals 2 end table


Dan


table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 cross times x subscript 2 end cell equals cell straight c over straight a end cell row blank equals cell fraction numerator negative 6 over denominator 2 end fraction end cell row blank equals cell negative 3 end cell end table


Sehingga diperoleh:


table attributes columnalign right center left columnspacing 0px end attributes row cell 1 over x subscript 1 squared plus 1 over x subscript 2 squared end cell equals cell fraction numerator x subscript 1 squared over denominator x subscript 1 squared times x subscript 2 squared end fraction plus fraction numerator x subscript 2 squared over denominator x subscript 1 squared times x subscript 2 squared end fraction end cell row blank equals cell fraction numerator x subscript 1 squared plus x subscript 2 squared over denominator open parentheses x subscript 1 times x subscript 2 close parentheses squared end fraction end cell end table


Ingat bahwa open parentheses x subscript 1 plus x subscript 2 close parentheses squared equals x subscript 1 squared plus 2 x subscript 1 times x subscript 2 plus x subscript 2 squared, sehingga:


table attributes columnalign right center left columnspacing 0px end attributes row cell 1 over x subscript 1 squared plus 1 over x subscript 2 squared end cell equals cell fraction numerator x subscript 1 squared over denominator x subscript 1 squared times x subscript 2 squared end fraction plus fraction numerator x subscript 2 squared over denominator x subscript 1 squared times x subscript 2 squared end fraction end cell row blank equals cell fraction numerator x subscript 1 squared plus x subscript 2 squared over denominator open parentheses x subscript 1 times x subscript 2 close parentheses squared end fraction end cell row blank equals cell fraction numerator open parentheses x subscript 1 plus x subscript 2 close parentheses squared minus 2 x subscript 1 times x subscript 2 over denominator open parentheses x subscript 1 times x subscript 2 close parentheses squared end fraction end cell row blank equals cell fraction numerator open parentheses 2 close parentheses squared minus 2 times left parenthesis negative 3 right parenthesis over denominator left parenthesis negative 3 right parenthesis squared end fraction end cell row blank equals cell fraction numerator 4 plus 6 over denominator 9 end fraction end cell row blank equals cell 10 over 9 end cell end table


Jadi, nilai 1 over x subscript 1 squared plus 1 over x subscript 2 squared equals 10 over 9.

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MUHAMMAD RAFFI ALGHIFARI

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