how-is-explanotory-solution-4-x-2-3x-2-4-x-2-3x-7-4-2x-2-6x-9-1-x-

Question Number 190907 by mustafazaheen last updated on 14/Apr/23

how is explanotory solution

4^{x^{2} + 3 x + 2} + 4^{x^{2} + 3 x + 7} = 4^{{2 x}^{2} + 6 x + 9} + 1

x = ?

Answered by Frix last updated on 14/Apr/23

4^{(x + 1) (x + 2)} + 4^{(x + 1) (x + 2) + 5} = 4^{2 (x + 1) (x + 2) + 5} + 1

t = 4^{(x + 1) (x + 2)}

t + 4^{5} t = 4^{5} t^{2} + 1

t^{2} - \frac{1025 t}{1024} + \frac{1}{1024} = 0

(t = \frac{1}{1024}) \lor t = 1

x \in R : x = - 2 \lor x = - 1

(x \notin R : x = - \frac{3}{2} \pm \frac{\sqrt{19}}{2} i)

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