Pertanyaan

Persamaan kuadrat 2 x 2 − p x + 1 = 0 dengan p > 0, mempunyai akar-akar α dan β . Jika x 2 − 5 x + q = 0 mempunyai akar-akar α 2 1 d an β 2 1 , maka q - p =…

Persamaan kuadrat $2 x^{2} - p x + 1 = 0$ dengan p > 0, mempunyai akar-akar α dan β. Jika $x^{2} - 5 x + q = 0$ mempunyai akar-akar $\frac{1}{α ^{2}} d an \frac{1}{β ^{2}}$ , maka q-p=…

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$2 x squared minus p x plus 1 equals 0 comma a k a r minus a k a r n y a space alpha space d a n space beta alpha plus beta equals negative b over a equals p over 2 alpha. beta equals c over a equals 1 half x squared minus 5 x plus q equals 0 comma a k a r minus a k a r n y a space 1 over alpha squared d a n 1 over beta squared 1 over alpha squared plus 1 over beta squared equals negative b over a fraction numerator alpha squared plus beta squared over denominator alpha squared beta squared end fraction equals 5 fraction numerator open parentheses alpha plus beta close parentheses squared minus 2 alpha beta over denominator open parentheses alpha beta close parentheses squared end fraction equals 5 fraction numerator open parentheses begin display style p over 2 end style close parentheses squared minus 2 open parentheses begin display style 1 half end style close parentheses over denominator open parentheses begin display style 1 half end style close parentheses squared end fraction equals 5 p squared over 4 minus 1 straight space equals 5 over 4 p squared minus 4 equals 5 p squared equals 9 p equals plus-or-minus 3 K a r e n a space p greater than 0 comma space m a k a space y a n g space d i a m b i l space p equals 3 1 over alpha squared. straight space 1 over beta squared equals c over a fraction numerator 1 over denominator alpha squared beta squared end fraction equals q fraction numerator 1 over denominator 1 fourth end fraction straight space equals q q equals 4 space J a d i comma space q minus p equals 4 minus 3 equals 1$