Za realne brojeve aa, bb i cc vrijedi

abc=1,a+b+c=4iabc = -1, \quad a + b + c = 4 \quad \text{i}

aa23a1+bb23b1+cc23c1=49.\frac{a}{a^2 - 3a - 1} + \frac{b}{b^2 - 3b - 1} + \frac{c}{c^2 - 3c - 1} = \frac{4}{9}.

Dokaži da je a2+b2+c2=332a^2 + b^2 + c^2 = \dfrac{33}{2}.