Pertanyaan

$\mathrm{Diketahui}\;\mathrm p\;\mathrm{dan}\;\mathrm q\;\mathrm{adalah}\;\mathrm{akar}-\mathrm{akar}\;\mathrm{persamaan}\;\mathrm{kuadrat}\;x^2\;\textemdash\;5x\;\textemdash\;6\;=\;0.\;\mathrm{Nilai}\;\mathrm{dari}\;p^2\;+\;q^2\;\textemdash\;4pq\;=\;...\;$

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$Ingat factorial Penjumlahan space dan space perkalian space akar minus akar space persamaan space kuadrat space a x squared plus b x plus c equals 0 space yang space memiliki space akar minus akar space straight x subscript 1 space dan space straight x subscript 2 comma space yaitu colon x subscript 1 plus x subscript 2 equals negative b over a x subscript 1. x subscript 2 equals c over a x subscript 1 superscript 2 plus x subscript 2 superscript 2 equals left parenthesis x subscript 1 plus x subscript 2 right parenthesis squared minus 2 x subscript 1. x subscript 2 Persamaan space kuadrat space x squared minus 5 x minus 6 equals 0 space dengan space akar minus akar space straight p space dan space straight q. Maka space nilai space dari colon p squared plus q squared minus 4 p q equals left parenthesis p plus q right parenthesis squared minus 2 p q minus 4 p q space space space space space space space space space space space space space space space space space space space space space space space equals left parenthesis p plus q right parenthesis squared minus 6 p q space space space space space space space space space space space space space space space space space space space space space space space equals open parentheses negative fraction numerator left parenthesis negative 5 right parenthesis over denominator 1 end fraction close parentheses squared minus 6 open parentheses fraction numerator open parentheses negative 6 close parentheses over denominator 1 end fraction close parentheses space space space space space space space space space space space space space space space space space space space space space space space equals 25 plus 36 space space space space space space space space space space space space space space space space space space space space space space space equals 61$