3. In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
- By substituting \(p = 3 ^ { x }\), show that the equation
$$3 \times 9 ^ { x } + 3 ^ { x + 2 } = 1 + 3 ^ { x - 1 }$$
can be rewritten in the form
$$9 p ^ { 2 } + 26 p - 3 = 0$$
- Hence solve
$$3 \times 9 ^ { x } + 3 ^ { x + 2 } = 1 + 3 ^ { x - 1 }$$