<s>[INST] Problem based on Algebraic identities Algebraic identities:
$$(a+b)^2 = a^2 + b^2 + 2ab$$
$$(a-b)^2 = a^2 + b^2 - 2ab$$
Other identities can also come to solve this question?
If $x + 1/x = 5$ and $x^2 + 1/x^3 = 8$, then what would be the value of $x^3 + 1/x^2$?
Possible answers:
a- 215
b- 125
c- 256
d- 525
 [/INST] we have $x^2+1=5x$ and $x^5+1=8x^3$
$$\frac{x^5+1}{x^2}=\frac{8x^3}{x^2}=8x$$
We need to solve for $x$  from $x^2-5x+1=0$ which will satisfy  $x^5+1=8x^3$ as well
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