- (i) Given that \(y = x ^ { \frac { 1 } { 3 } }\), show that the equation
$$2 x ^ { \frac { 1 } { 3 } } + 3 x ^ { - \frac { 1 } { 3 } } = 7$$
can be rewritten as
$$2 y ^ { 2 } - 7 y + 3 = 0 .$$
(ii) Hence, solve the equation
$$2 x ^ { \frac { 1 } { 3 } } + 3 x ^ { - \frac { 1 } { 3 } } = 7$$