Question

find x³ - y³, if x - y = 5 and xy = 15

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Answer 1

Answer:

x + y = 12

Raise both sides to the 3rd power (cube both sides)

(x + y)³ = 12³

(x + y)(x + y)(x + y) = 1728

(x + y)(x² + 2xy + y²) = 1728

x³ + 2x²y + xy² + x²y +2xy² + y³ = 1728

x³ + 3x²y + 3xy² + y³ = 1728

Factor 3xy out of the two middle terms:

x³ + 3xy(x + y) + y³ = 1728

We substitute 27 for xy and 12 for x + y

x³ + 3(27)(12) + y³ = 1728

x³ + 972 + y³ = 1728

x³ + y³ = 756

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