Question : a³ + b³ + c³ = 3abc if _________.

Option 1: a = b = c

Option 2: a + b + c = 0

Option 3: a + b + c = 1

Option 4: a + b + c = –1

Question : What is the value of ${a}^3+{b}^3+{c}^3$ if $(a+b+c)=0$?

Option 1: $a^2+b^2+c^2-3abc$

Option 2: $0$

Option 3: $3abc$

Option 4: $a^2+b^2+c^2-ab-bc-ca$

Question : If a( a + b + c) = 45, b( a + b + c) = 75, and c( a + b + c) =105, then what is the value of a² + b² + c²?

Option 1: 75

Option 2: 83

Option 3: 217

Option 4: 225

Question : What is the possible value of (a + b + c) – 3, if a² + b² + c² = 9 and ab + bc + ca = 8?

Option 1: 5

Option 2: 3

Option 3: 9

Option 4: 2

Question : If $a+\frac{1}{b}=b+\frac{1}{c}=c+\frac{1}{a}$ where $a \neq b\neq c\neq 0$, then the value of $a^{2}b^{2}c^{2}$ is:

Option 1: –1

Option 2: abc

Option 3: 0

Option 4: 1