Jika x1 dan x2 akar akar persamaan kuadrat x^2-3x+1=0,maka persamaan kuadrat yang akar akarnya x1+1/x1 dan x2+1/x2 adalah?

x² - 3x + 1 = 0 akarakar x1 & x2
x1 + x2 = 3
x1 × x2 = 1

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[tex]x1 + \frac{1}{x1} + x2 + \frac{1}{x2} \\ = x1 + x2 + \frac{x1 + x2}{x1 \times x2} \\ = 3 + \frac{3}{1} \\ = 6[/tex]
[tex](x1 + \frac{1}{x1} )(x2 + \frac{1}{x2} ) \\ = (x1 \times x2) + \frac{x1}{x2} + \frac{x2}{x1} + \frac{1}{x1 \times x2 } \\ = 1 + \frac{ {3}^{2} - 2 } {1} + 1 \\ = 9[/tex]
PK BARU
X2 - 6X + 9 = 0