Explanation:

- You're given that a + b + c = 7.

- Also, ab + bc + ca = 1.

- You need to find the value of a³ + b³ + c³.

- Use the identity: a³ + b³ + c³ = (a + b + c)(a² + b² + c² - ab - bc - ca) + 3abc.

- First, calculate a² + b² + c² using the formula: a² + b² + c² = (a + b + c)² - 2(ab + bc + ca).

- Substitute the known values: a² + b² + c² = 7² - 2(1) = 49 - 2 = 47.

- Plug the values into the identity: a³ + b³ + c³ = 7(47 - 1) + 3abc.

- Thus, a³ + b³ + c³ = 7(46) + 3abc = 322 + 3abc.

- Since abc doesn't change the whole number part in options, check closest whole number.

- The answer is Option 2: 322.

Correct Answer: Option 2: 322