Question

Suppose that the demand equation for a certain item is 1p+1x2−160=0. evaluate the elasticity at 65:

Answer 1

Price elasticity is defined as $\frac{\Delta(quantity)}{\Delta(price)}$.

Here, the question has omitted to define variables, so we will ASSUME
p=price
x=variable,
and we're given
p+x^2-160=0

We calculate
$\delta{x}/\delta{p}$ by implicit differentiation with respect to p:
1+2x (dx/dp)=0
=>
E(x)=(dx/dp)=-1/(2x)

Therefore the price elasticity at x=65 is
E(65)=1/(2*65) =-1/130 (approximately -0.00769)