Quiz Matematika Materi : Variabel Kelas : X SMA Diffucilties : Easy Soal : Diberikan [tex] x+ \frac {1}{x} = 3 [/tex] Tanpa harus mencari nilai [tex] x – ny

Materi Analisis Bentuk Pangkat

[tex] \displaystyle x + \frac{1}{x} = 3 \\ (x + \frac{1}{x})^2 = 9 \\ x^2 + \frac{1}{x^2} = 7 \\ (x^2 + \frac{1}{x^2})^3 = 7^3 \\ (x^6 + \frac{1}{x^6}) + 3(x^2 + \frac{1}{x^2}) = 343 \\ x^6 + \frac{1}{x^6} = 343 - 3(7) = 322 \\ \text{Dengan demikian} \\ (x^2 + \frac{1}{x^2})^5 = 7^5 \\ (x^{10} + \frac{1}{x^{10}}) + 5(x^6 + \frac{1}{x^6}) + 10(x^2 + \frac{1}{x^2}) = 16807 \\ x^{10} + \frac{1}{x^{10}} + 5(322) + 10(7) = 16807 \\ x^{10} + \frac{1}{x^{10}}= 15127 [/tex]