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Diketahui α dan β adalah akar−akar persamaan kuadrat 3x2−x−2=0. Nilai dari  α2+β2+αβ= ....

Pertanyaan

Diketahui space straight alpha space dan space straight beta space adalah space akar minus akar space persamaan space kuadrat space 3 straight x squared minus straight x minus 2 equals 0. space Nilai space dari space space straight alpha squared plus straight beta squared plus αβ equals space....

  1. 7 over 9

  2. 8 over 9

  3. 1

  4. 10 over 9

  5. 11 over 9

Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

U n t u k space p e r s a m a a n space k u a d r a t space a x squared plus b x plus c equals 0 space y a n g space m e m i l i k i space a k a r space alpha space d a n space beta comma m a k a  alpha plus beta equals fraction numerator negative b over denominator a end fraction  alpha beta equals c over a

P e r s a m a a n space k u a d r a t space 3 x squared minus x minus 2 equals 0 space d e n g a n space a equals 3 comma space b equals negative 1 space d a n space c equals negative 2 comma space m e m i l i k i space a k a r minus a k a r space alpha space d a n space beta comma space m a k a  alpha plus beta equals negative b over a equals 1 third  alpha beta equals c over a equals negative 2 over 3

N i l a i space d a r i space alpha squared plus beta squared plus alpha beta  equals left parenthesis alpha plus beta right parenthesis squared minus 2 alpha beta plus alpha beta  equals left parenthesis alpha plus beta right parenthesis squared minus alpha beta  equals open parentheses 1 third close parentheses squared minus open parentheses negative 2 over 3 close parentheses  equals open parentheses 1 over 9 close parentheses plus 2 over 3  equals 7 over 9

 

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Jika x1​ dan x2​ adalah akar-akar persamaan kuadrat x2+mx+n=0 dengan x1​+x2​=4 dan x1​x2​=2, maka nilai x1​−x2​ adalah ....

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