Question : If a + b + c = 1, ab + bc + ca = –22 and abc = –40, then what is the value of a³ + b³ + c³ ?

Option 1: 67

Option 2: –53

Option 3: –51

Option 4: 27

Question : If (a + b + c) = 12 and (ab + bc + ca) = 47, find the value of (a³ + b³ + c³ – 3abc).

Option 1: 24

Option 2: 36

Option 3: 48

Option 4: 42

Question : What is the value of a² + b² + c², if a + b + c = 9 and ab + bc + ca = 23 ?

Option 1: 22

Option 2: 32

Option 3: 49

Option 4: 35

Question : If $\frac{a^{2} - bc}{a^{2}+bc}+\frac{b^{2}-ca}{b^{2}+ca}+\frac{c^{2}-ab}{c^{2}+ab}=1$, then the value of $\frac{a^{2}}{a^{2}+bc}+\frac{b^{2}}{b^{2}+ac}+\frac{c^{2}}{c^{2}+ab}$ is:

Option 1: 0

Option 2: 1

Option 3: –1

Option 4: 2

Question : a³ – b³ = 91 and a – b = 1, what is the value of (ab)?

Option 1: 27

Option 2: 6

Option 3: 9

Option 4: 30