Given that \(y = 2 ^ { x }\), show that the equation
$$2 ^ { x } + 3 \left( 2 ^ { - x } \right) = 4$$
can be written in the form
$$y ^ { 2 } - 4 y + 3 = 0$$
Hence solve the equation
$$2 ^ { x } + 3 \left( 2 ^ { - x } \right) = 4$$
giving the values of \(x\) correct to 3 significant figures where appropriate.