Question

ecuatie exponentiala:
7*4^(x^2)+2*49^(x^2)=9*14^(x^2)

Answer 1

7·(2²)ˣ²+2·(7²)ˣ²=9·(7·2)ˣ²
7·2²ˣ²+2·7²ˣ²=9·7ˣ²·2ˣ²se imparte toata ecuatia la 7ˣ²·2ˣ²
7·2²ˣ²/7ˣ²·2ˣ²+2·7²ˣ²/7ˣ²·2ˣ²=9
7·(2/7)ˣ²+2·(7/2)ˣ²=9
inlocuim pe (2/7)ˣ²=y
7y+2·1/y=9
7y²-9y+2=0
Δ=81-56=25
√Δ=5
y₁=(9+5)/14=14/14=1
y₂=(9-5)/14=4/14=2/7

(2/7)ˣ²=y₁
(2/7)ˣ²=1
(2/7)ˣ²=(2/7)⁰
x²=0
x₁=x₂=0

(2/7)ˣ²=y₂
(2/7)ˣ²=(2/7)
x²=1
x²-1=0
(x-1((x+1)=0
x₃=1
x₄=-1