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Multiple Choice Questions

If x y 4 then what is the value of x3 y3 12xy Options ........

Quantitative Aptitude (CPO) Algebra

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

Options:

256

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Explanation:

- 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** ✅

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