Pertanyaan

Jika x 1 , x 2 adalah akar-akar dari persamaan x 2 − 2 x + 3 = 0 , maka nilai x 1 2 x 2 + x 2 2 x 1 = …

Jika $x_{1}, x_{2}$ adalah akar-akar dari persamaan $x^{2} - 2 x + 3 = 0$ , maka nilai $\frac{x _{2}}{x _{1}^{2}} + \frac{x _{1}}{x _{2}^{2}} = \dots$

A. C

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Jawaban terverifikasi

Pembahasan

Ingat kembali: Jika memiliki akar dan maka

Ingat kembali:

Jika memiliki akar dan maka
$x subscript 1 plus x subscript 2 equals negative b over a x subscript 1 x subscript 2 equals c over a x squared minus 2 x plus 3 equals 0 x subscript 1 plus x subscript 2 equals negative fraction numerator open parentheses negative 2 close parentheses over denominator 1 end fraction equals 2 x subscript 1 space x subscript 2 equals 3 over 1 equals 3 fraction numerator x subscript 2 over denominator x subscript 1 superscript 2 end fraction plus fraction numerator x subscript 1 over denominator x subscript 2 superscript 2 end fraction equals fraction numerator x subscript 1 superscript 3 plus x subscript 2 superscript 3 over denominator x subscript 1 superscript 2 space x subscript 2 superscript 2 end fraction equals fraction numerator open parentheses x subscript 1 plus x subscript 2 close parentheses cubed minus 3 left parenthesis x subscript 1 x subscript 2 right parenthesis left parenthesis x subscript 1 plus x subscript 2 right parenthesis over denominator open parentheses x subscript 1 x subscript 2 close parentheses squared end fraction equals fraction numerator open parentheses 2 close parentheses cubed minus 3 open parentheses 3 close parentheses open parentheses 2 close parentheses over denominator open parentheses 3 close parentheses squared end fraction equals fraction numerator 8 minus 18 over denominator 9 end fraction equals negative 10 over 9$