Pertanyaan

Diketahui x + x 1 = 7 . Jika x 4 + x 2 + 1 A x 2 = 6 5 , maka nilai A = ...

Diketahui $x + \frac{1}{x} = 7$ . Jika $\frac{A x ^{2}}{x ^{4} + x ^{2} + 1} = \frac{5}{6}$ , maka nilai A = ...

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N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Diketahui Selanjutnya:

Diketahui

x plus 1 over x equals 7 left right double arrow open parentheses x plus 1 over x close parentheses squared equals 7 squared left right double arrow x squared plus 2 plus 1 over x squared equals 49 left right double arrow x squared plus 1 over x squared equals 47 left right double arrow x to the power of 4 plus 1 equals 47 x squared

Selanjutnya:

$fraction numerator A x squared over denominator x to the power of 4 plus x squared plus 1 end fraction equals 5 over 6 left right double arrow fraction numerator A x squared over denominator open parentheses x to the power of 4 plus 1 close parentheses plus x squared end fraction equals 5 over 6 left right double arrow fraction numerator A x squared over denominator 47 x squared plus x squared end fraction equals 5 over 6 left right double arrow A over 48 equals 5 over 6 left right double arrow A equals 5 over 6 cross times 48 left right double arrow A equals 40$