Let z {\displaystyle \displaystyle z} be the same implicit function as in part (ii), defined by the equation x 2 z 3 + y sin ( π x ) = − y 2 {\displaystyle \displaystyle x^{2}z^{3}+y\sin(\pi x)=-y^{2}} . Let x = 0.97 {\displaystyle \displaystyle x=0.97} , and y = 1 {\displaystyle \displaystyle y=1} . Find the approximate value of z {\displaystyle \displaystyle z} .
