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Diketahui dan adalah akar-akar persamaan kuadrat berikut. Tentukan nilai , , , dan .

Pertanyaan

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

Pembahasan Soal:

Persamaan kuadrat size 14px x to the power of size 14px 2 size 14px plus size 14px 3 size 14px x size 14px minus size 14px 2 size 14px equals size 14px 0

 Diketahui: size 14px a size 14px equals size 14px 1 size 14px comma size 14px space size 14px b size 14px equals size 14px 3 size 14px comma size 14px space size 14px c size 14px equals size 14px minus size 14px 2

 size 14px alpha size 14px plus size 14px beta size 14px equals fraction numerator size 14px minus size 14px b over denominator size 14px a end fraction size 14px equals fraction numerator size 14px minus size 14px 3 over denominator size 14px 1 end fraction size 14px equals size 14px minus size 14px 3 

size 14px alpha size 14px. size 14px beta size 14px equals size 14px c over size 14px a size 14px equals fraction numerator size 14px minus size 14px left parenthesis size 14px minus size 14px 2 size 14px right parenthesis over denominator size 14px 1 end fraction size 14px equals size 14px 2

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 negative 3 over 2 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 negative 3 right parenthesis squared minus 2 left parenthesis 2 right parenthesis equals 9 plus 4 equals 13 end style 

 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 03 Februari 2021

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