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I appreciate your math skills however over 80-90% of the privileges are identical. Every problem has one number that is the square of the other leading to a simple quadratic equation😮.😮😮
At a quick glance I start this by writing the equation 2^a + 2^2a = 2 ^3a. I see this already in the comments below.
2ⁿ+4ⁿ=8ⁿ2ⁿ+(2ⁿ)²=(2ⁿ)³Let ∆=2ⁿ∆+∆²=∆³∆³-∆²-∆=0∆(∆²-∆-1)=0∆=02ⁿ=0 reject∆²-∆-1=04∆²-4∆-4=04∆²-4∆+1=5(2∆-1)²=5|2∆-1|=√52∆-1=-√52∆=1-√5∆=½(1-√5)2ⁿ=½(1-√5)
I appreciate your math skills however over 80-90% of the privileges are identical. Every problem has one number that is the square of the other leading to a simple quadratic equation😮.😮😮
At a quick glance I start this by writing the equation 2^a + 2^2a = 2 ^3a. I see this already in the comments below.
2ⁿ+4ⁿ=8ⁿ
2ⁿ+(2ⁿ)²=(2ⁿ)³
Let ∆=2ⁿ
∆+∆²=∆³
∆³-∆²-∆=0
∆(∆²-∆-1)=0
∆=0
2ⁿ=0 reject
∆²-∆-1=0
4∆²-4∆-4=0
4∆²-4∆+1=5
(2∆-1)²=5
|2∆-1|=√5
2∆-1=-√5
2∆=1-√5
∆=½(1-√5)
2ⁿ=½(1-√5)