Pertanyaan

Persamaan kuadrat x 2 − a x + 1 = 0 mempunyai akar x 1 dan x 2 . Jika persamaan kuadrat x 2 + p x + q = 0 mempunyai akar x 2 x 1 3 dan x 1 x 2 3 , maka p = .....

Persamaan kuadrat $x^{2} - a x + 1 = 0$ mempunyai akar $x_{1}$ dan $x_{2}$ . Jika persamaan kuadrat $x^{2} + p x + q = 0$ mempunyai akar $\frac{x _{1}^{3}}{x _{2}}$ dan $\frac{x _{2}^{3}}{x _{1}}$ , maka p = .....

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Persamaan Kuadrat

$P e r s a m a a n space x squared space minus space a x space plus space 1 space equals space 0 x subscript 1 plus x subscript 2 equals negative b over a equals negative fraction numerator left parenthesis negative a right parenthesis over denominator 1 end fraction equals a x subscript 1 times x subscript 2 equals c over a equals 1 over 1 equals 1 P e r s a m a a n space d e n g a n space a k a r space x subscript 1 cubed over x subscript 2 space d a n space x subscript 2 cubed over x subscript 1 P e r s a m a a n space u m u m space d a r i space p e r s a m a a n space k u a d r a t x squared space minus space left parenthesis x subscript 1 space plus space x subscript 2 space right parenthesis x space plus space left parenthesis x subscript 1 space times space x subscript 2 space right parenthesis equals space 0 x subscript 1 plus x subscript 2 equals x subscript 1 cubed over x subscript 2 plus x subscript 2 cubed over x subscript 1 space space space space space space space space space space space space equals fraction numerator x subscript 1 to the power of 4 plus x subscript 2 to the power of 4 space over denominator x subscript 1 x subscript 2 end fraction space space space space space space space space space space space space equals space fraction numerator left parenthesis x subscript 1 squared space plus space x subscript 2 squared space right parenthesis squared space minus space 2 x subscript 1 squared space x subscript 2 squared space space over denominator x subscript 1 x subscript 2 end fraction space space space space space space space space space space space space equals fraction numerator left parenthesis a squared minus 2 right parenthesis squared space minus space 2 over denominator 1 end fraction space space space space space space space space space space space space equals a to the power of 4 space minus space 4 a squared space plus space 2$

$x subscript 1 times x subscript 2 equals x subscript 1 times x subscript 2 equals x subscript 1 cubed over x subscript 2 times x subscript 2 cubed over x subscript 1 equals fraction numerator left parenthesis x subscript 1. x subscript 2 right parenthesis cubed over denominator x subscript 1. x subscript 2 end fraction equals 1 cubed over 1 equals 1 x squared minus left parenthesis x subscript 1 plus x subscript 2 right parenthesis x plus left parenthesis x subscript 1. x subscript 2 right parenthesis equals 0 x squared minus left parenthesis a to the power of 4 minus 4 a squared plus 2 right parenthesis x plus 1 equals 0 space M a k a space p equals negative a to the power of 4 plus 4 a squared minus 2$