218 4) 2ˣ⁺¹ + 3 ⋅ 2ˣ⁻¹ - 5 ⋅ 2ˣ + 6 = 0.

4) 2ˣ⁺¹ + 3 ⋅ 2ˣ⁻¹ - 5 ⋅ 2ˣ + 6 = 0

$$2^x \cdot 2 + 3 \cdot \frac{2^x}{2} - 5 \cdot 2^x + 6 = 0$$

$$2^x(2 + \frac{3}{2} - 5) + 6 = 0$$

$$2^x(\frac{4 + 3 - 10}{2}) + 6 = 0$$

$$2^x(\frac{-3}{2}) + 6 = 0$$

$$- \frac{3}{2} 2^x = -6$$

$$2^x = \frac{-6 \cdot 2}{-3} = 4$$

$$2^x = 2^2$$

$$x = 2$$

Ответ: 2