Find the sum of their cubes.

If the sum and the product of two numbers are 8 and 15 respectively, find the sum of their cubes.

Answer :

Consider x and y as the two numbers

x + y = 8 and xy = 15

By cubing on both sides

(x + y)³ = 8³

Expanding using formula

x³ + y³ + 3xy (x + y) = 512

Substituting the values

x³ + y³ + 3 × 15 × 8 = 512

By further calculation

x³ + y³ + 360 = 512

So we get

x³ + y³ = 512 – 360 = 152

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