Za realne brojeve aaa, bbb i ccc vrijedi
abc=−1,a+b+c=4iabc = -1, \quad a + b + c = 4 \quad \text{i}abc=−1,a+b+c=4i
aa2−3a−1+bb2−3b−1+cc2−3c−1=49.\frac{a}{a^2 - 3a - 1} + \frac{b}{b^2 - 3b - 1} + \frac{c}{c^2 - 3c - 1} = \frac{4}{9}.a2−3a−1a+b2−3b−1b+c2−3c−1c=94.
Dokaži da je a2+b2+c2=332a^2 + b^2 + c^2 = \dfrac{33}{2}a2+b2+c2=233.