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Diketahui dan adalah akar-akar persamaan kuadrat b...

Diketahui begin mathsize 14px style alpha end style dan begin mathsize 14px style beta end style adalah akar-akar persamaan kuadrat berikut. Tentukan nilai begin mathsize 14px style alpha plus beta end style, begin mathsize 14px style alpha times beta end style, begin mathsize 14px style 1 over alpha plus 1 over beta end style, dan begin mathsize 14px style alpha squared plus beta squared end style.

  1. begin mathsize 14px style... end style

  2. undefined

Jawaban:

Persamaan kuadrat begin mathsize 14px style 2 x squared minus 8 x plus 3 equals 0 end style 

Diketahui: begin mathsize 14px style a equals 2 comma space b equals negative 8 comma space c equals 3 end style 

Penyelesaian:

begin mathsize 14px style alpha plus beta equals fraction numerator negative b over denominator a end fraction equals fraction numerator negative left parenthesis negative 8 right parenthesis over denominator 2 end fraction equals 8 over 2 equals 4 end style 

begin mathsize 14px style alpha. beta equals c over a equals 3 over 2 end style 

begin mathsize 14px style 1 over alpha plus 1 over beta equals fraction numerator beta plus alpha over denominator alpha. beta end fraction equals fraction numerator alpha plus beta over denominator alpha. beta end fraction equals fraction numerator 4 over denominator begin display style 3 over 2 end style end fraction equals 4 cross times 2 over 3 equals 8 over 3 end style 

begin mathsize 14px style alpha squared plus beta squared equals left parenthesis alpha plus beta right parenthesis squared minus 2 left parenthesis alpha. beta right parenthesis equals left parenthesis 4 right parenthesis squared minus 2 left parenthesis 3 over 2 right parenthesis equals 16 minus 3 equals 13 end style 

 

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