Algebra

Quantitative Aptitude (CPO)

Title

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Indian Economy - Understanding the basics of Indian economic system

If x + y = 4, then what is the value of x³ + y³ + 12xy?

Options:

256

- We are given the equation: \(x + y = 4\).

- We need to find: \(x^3 + y^3 + 12xy\).

- Using the identity for cube sums: \(x^3 + y^3 = (x + y)(x^2 - xy + y^2)\).

- Substitute: \(x^3 + y^3 = 4(x^2 - xy + y^2)\).

- We also know: \(x^2 - xy + y^2 = (x + y)^2 - 3xy\).

- Substitute: \(x^2 - xy + y^2 = 16 - 3xy\).

- So: \(x^3 + y^3 = 4(16 - 3xy) = 64 - 12xy\).

- Thus, \(x^3 + y^3 + 12xy = 64 - 12xy + 12xy = 64\).

- Answer: 64