d
(d) \({4^{({x^2} + 2)}} - {9.2^{({x^2} + 2)}} + 8 = 0\)

\( \Rightarrow {\left( {{2^{({x^2} + 2)}}} \right)^2} - {9.2^{({x^2} + 2)}} + 8 = 0\)

Put \({2^{({x^2} + 2)}}^2 = y\). Then \({y^2} - 9y + 8 = 0\), which gives \(y = 8,y = 1\).

when \(y = 8\,\, \Rightarrow \,\,{2^{{x^2} + 2}} = 8\) ==> \({2^{{x^2} + 2}} = {2^3}\)

==> \({x^2} + 2 = 3\)

==> \({x^2} = 1\) ==>\(x = 1, - 1\).

when \(y = 1\) ==> \({2^{{x^2} + 2}} = 1\) ==> \({2^{{x^2} + 2}} = {2^o}\)

==> \({x^2} + 2 = 0\) ==>\({x^2} = - 2\), which is not possible.