Kuis +50 poin kexcvi :, Cari nilai x dari, , (ngasal, report)

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Kuis +50 poin kexcvi :


Cari nilai x dari
\displaystyle\huge\boxed{\sf{\frac{1^{x+1^{x+1^x}}}{x+\frac{1}{x+\frac{1}{x}}}=\frac{10}{9}}}
(ngasal, report)

Aljabar

Penyebut

B = x + 1/(x + 1/x)

B = x + x/(x² + 1)

B = (x³ + 2x)/(x² + 1)

Pembilang

A = 1^(x + 1^(x + 1^x))

utk x ∈ R dan x ≠ 0

A = 1

soal = A/B = 10/9

1/B = 10/9

B = 9/10

(x³ + 2x)/(x² + 1) = 9/10

10x³ + 20x = 9x² + 9

10x³ – 9x² + 20x – 9 = 0

(2x – 1)(5x² – 2x + 9) = 0

x = 1/2 → akar real

Nilai x = 1/2


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