Question

x+y = 12, xy = 27 find x^3 + y^3

Answer 1

applying the identity
(x+y)^3=x3+y3+3xy(x+y)
(12)3=x3+y3+3×27(12)
1728=x3+y3+972
1728-972=x3+y3
756=x3+y3

Answer 2

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$= > given \: \\ = > x + y \: = 12 \\ = > xy = 27 \\ \\ to \: find \: {x}^{3} + {y}^{3} \\ \\ solution \: \\ \\ = > {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y) \\ \\=> (12 )^3 = > { x }^{3} + {y}^{3} + 3 \times 27 \times 12 \\ \\ => 1728 = > {x}^{3} + {y}^{3} + 972$

=> x^3 + y^3 = 1728 - 972

=> x^3 + y^3 = 756

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