Pertanyaan

Jika dan adalah akar-akar persamaan dan α β β α α α β β = 32 1 , nilai dari α 3 + β 3 = …

Jika dan adalah akar-akar persamaan dan $α^{β} β^{α} α^{α} β^{β} = \frac{1}{32}$ , nilai dari $α^{3} + β^{3} = \dots$

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A. C

Master Teacher

Jawaban terverifikasi

Pembahasan

Ingat Kembali: Jadi memiliki akar dan maka:

Ingat Kembali:

Jadi memiliki akar dan maka:

$x subscript 1 plus x subscript 2 equals negative b over a x subscript 1 space x subscript 2 equals c over a b x squared plus open parentheses b minus 8 close parentheses x plus 2 b equals 0 alpha plus beta equals negative fraction numerator open parentheses b minus 8 close parentheses over denominator b end fraction equals fraction numerator negative b plus 8 over denominator b end fraction alpha beta equals fraction numerator 2 b over denominator b end fraction equals 2 alpha to the power of beta beta to the power of alpha alpha to the power of alpha beta to the power of beta equals 1 over 32 alpha to the power of alpha plus beta end exponent beta to the power of alpha plus beta end exponent equals 1 over 32 open parentheses alpha beta close parentheses to the power of alpha plus beta end exponent equals 1 over 2 to the power of 5 open parentheses 2 close parentheses to the power of fraction numerator negative b plus 8 over denominator b end fraction end exponent equals 2 to the power of negative 5 end exponent fraction numerator negative b plus 8 over denominator b end fraction equals negative 5 minus b plus 8 equals negative 5 b 4 b equals space minus 8 b equals space minus 2 alpha plus beta equals fraction numerator negative b plus 8 over denominator b end fraction equals fraction numerator 2 plus 8 over denominator negative 2 end fraction equals negative 5$