f(x)=\sqrt3x^2-(2\sqrt3+1)x+\sqrt2
a=\sqrt3 , b=2\sqrt3+1 , c=\sqrt2
x_1=\frac{-b}{a}
x_2=\frac{c}{a}
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{x_1}^2=(\frac{(2\sqrt3+1)}{\sqrt3})^2=\frac{(2\sqrt3+1)^2}{3}=\frac{4*3+4\sqrt3+1}{3}=\frac{13+4\sqrt3}{3}
{x_2}^2=(\frac{c}{a})^2=(\frac{\sqrt2}{\sqrt3})^2=\frac{2}{3}
1)
{x_1}^2+{x_2}^2=\frac{13+4\sqrt3}{3}+\frac{2}{3}=\frac{13+4\sqrt3+2}{3}=\frac{15+4\sqrt3}{3}
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\frac{1}{{x_1}^2}+\frac{1}{{x_2}^2}