[tex] \text{Nilai dari } \: 9x^2+\frac{1}{x^2} \: \text{ adalah } \: 19 \: \: (a) \: . [/tex]
[tex] \begin{aligned} 3x + \frac{1}{x} & \: = 5 \\ \\ \left(3x + \frac{1}{x}\right)^2 \: & = 5^2 \\ \\ 9x^2+6+\frac{1}{x^2} \: & = 25 \\ \\ 9x^2+\frac{1}{x^2} +6 \: & = 25 \\ \\ 9x^2+\frac{1}{x^2} +6-6 \: & = 25-6 \\ \\ 9x^2+\frac{1}{x^2} \: & = 19 \\ \\ \end{aligned} [/tex]
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[tex] \text{Nilai dari } \: 9x^2+\frac{1}{x^2} \: \text{ adalah } \: 19 \: \: (a) \: . [/tex]
Pembahasan
[tex] \begin{aligned} 3x + \frac{1}{x} & \: = 5 \\ \\ \left(3x + \frac{1}{x}\right)^2 \: & = 5^2 \\ \\ 9x^2+6+\frac{1}{x^2} \: & = 25 \\ \\ 9x^2+\frac{1}{x^2} +6 \: & = 25 \\ \\ 9x^2+\frac{1}{x^2} +6-6 \: & = 25-6 \\ \\ 9x^2+\frac{1}{x^2} \: & = 19 \\ \\ \end{aligned} [/tex]
Kesimpulan :
[tex] \text{Nilai dari } \: 9x^2+\frac{1}{x^2} \: \text{ adalah } \: 19 \: \: (a) \: . [/tex]