Question : If $x^{3}-y^{3}=81$ and $x-y=3$, what is the value of $x^{2}+y^{2}$?
Option 1: 18
Option 2: 21
Option 3: 27
Option 4: 36
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Correct Answer: 21
Solution : Given: $x^{3}-y^{3}=81$ and $x-y=3$ We know, $x^{3}-y^{3}=(x-y)^{3}+3xy(x-y)$ Substituting the values of $x^{3}-y^{3}$ and $x-y$, we get, $81=3^{3}+3×3xy$ $⇒xy=6$ Now, $x^{2}+y^{2}=(x-y)^{2}+2xy=3^{2}+2\times 6=21$ Hence, the correct answer is 21.
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Question : What is the value of $64 x^3+38 x^2 y+20 x y^2+y^3$, when $x=3$ and $y=-4$?
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