MCQ
If $x+y=12$ and $x y=27$, then $x^3+y^3=$
- A765
- B756
- C657
- D675
✓
Answer
B. 756
We know that
$\begin{array}{ll}\therefore & x^3+y^3=(x+y)\left(x^2-x y+y^2\right) \\ \Rightarrow & x^3+y^3=(x+y)\left\{\left((x+y)^2-3 x y\right)\right\}=12\left(12^2-3 \times 27\right)=12(144-81)=756\end{array}$
We know that
$\begin{array}{ll}\therefore & x^3+y^3=(x+y)\left(x^2-x y+y^2\right) \\ \Rightarrow & x^3+y^3=(x+y)\left\{\left((x+y)^2-3 x y\right)\right\}=12\left(12^2-3 \times 27\right)=12(144-81)=756\end{array}$
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