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Akar-akar dari persamaan 2 x 2 − 3 x − 9 = 0 adalah x 1 dan x 2 . Nilai dari x 1 2 + x 2 2 adalah...

Akar-akar dari persamaan $2 x^{2} - 3 x - 9 = 0$ adalah $x_{1}$ dan $x_{2}$ . Nilai dari $x_{1}^{2} + x_{2}^{2}$ adalah...

R. RGFLSATU

Master Teacher

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$2 x squared minus 3 x minus 9 equals 0 rightwards arrow a equals 2 comma space b equals negative 3 comma space c equals negative 9 x 1 plus x 2 equals fraction numerator negative b over denominator a end fraction equals fraction numerator negative left parenthesis negative 3 right parenthesis over denominator 2 end fraction equals 3 over 2 x 1 times x 2 equals c over a equals fraction numerator negative 9 over denominator 2 end fraction x subscript 1 squared plus x subscript 2 squared equals left parenthesis x subscript 1 plus x subscript 2 right parenthesis squared minus 2 left parenthesis x subscript 1. x subscript 2 right parenthesis space space space space space space space space space space space space space space space equals open parentheses 3 over 2 close parentheses squared minus 2 open parentheses fraction numerator negative 9 over denominator 2 end fraction close parentheses equals 9 over 4 plus 9 space space space space space space space space space space space space space space space equals 45 over 4 equals 11 1 fourth$