1-2-3 معادلات تحتاج إلى عامل مشترك

مثال 1: حل 2ˣ + 2ˣ⁺¹ = 24.

الحل:

2ˣ + 2ˣ × 2 = 24

2ˣ\[\begin{gathered}(1 + 2) = 24\end{gathered}\]

3 × 2ˣ = 24

2ˣ = 8 = 2³

x = 3

مثال 2: حل 3ˣ⁺² − 3ˣ = 72.

الحل:

3ˣ × 9 − 3ˣ = 72

3ˣ\[\begin{gathered}(9 - 1) = 72\end{gathered}\]

8 × 3ˣ = 72

3ˣ = 9 = 3²

x = 2

مثال 3: حل 5ˣ⁺¹ + 5ˣ = 150.

الحل:

5ˣ × 5 + 5ˣ = 150

6 × 5ˣ = 150

5ˣ = 25 = 5²

x = 2

مثال 4: حل 2ˣ⁺² + 2ˣ = 20.

الحل:

4 × 2ˣ + 2ˣ = 20

5 × 2ˣ = 20

2ˣ = 4

x = 2