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Question

If $$x+y=12$$ and $$xy=27$$, find the value of $$x^3+y^3$$.


Solution

Given that, $$x+y=12$$ and $$xy=27$$

We know,

$$(x+y)^3=x^3+y^3+3xy(x+y)$$

Therefore,

$$12^3=x^3+y^3+3\times 27\times 12$$

$$1728=x^3+y^3+972$$

$$x^3+y^3=1728-972=756$$

$$\therefore x^3+y^3=756$$

Mathematics

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