Sum of Cubes Identity

CMAT 2022 · Quantitative Techniques & Data Interpretation · Easy · Algebra

If $(x + y) = 3$ and $xy = 2$ , then what is the value of $x^3 + y^3$ ?

Answer

We know $x^3 + y^3 = (x + y)^3 - 3xy(x + y)$ . Substitute $(x + y) = 3$ and $xy = 2$ : $x^3 + y^3 = 3^3 - 3(2)(3) = 27 - 18 = 9$ .

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