По теореме Виета:

[tex]a{x}^{2} + bx + c = 0 \\ x _{1} + x_{2} = - \frac{b}{a} \\ x _{1} x_{2} = \frac{c}{a} [/tex]

[tex] {4x}^{2} - 9x + 3 = 0 \\ x _{1} + x_{2} = - \frac{ - 9}{4} = \frac{9}{4} \\ x _{1} x_{2} = \frac{3}{4} \\ \\ \frac{1}{x_{1}} + \frac{1}{x_{2}} = \frac{x _{2}+ x_{1}}{x_{1}x_{2}} = \\ \frac{9}{4} \div \frac{3}{4} = \frac{9 \times 4}{4 \times 3} = 3[/tex]

Отве: 3