When the two roots of the equation $4 ^ { x } - 7 \cdot 2 ^ { x } + 12 = 0$ are $\alpha , \beta$, find the value of $2 ^ { 2 \alpha } + 2 ^ { 2 \beta }$. [3 points]
When the two roots of the equation $4 ^ { x } - 7 \cdot 2 ^ { x } + 12 = 0$ are $\alpha , \beta$, find the value of $2 ^ { 2 \alpha } + 2 ^ { 2 \beta }$. [3 points]