Показательные уравнения:
1. (1/3)^2x = 162 - (1/3)^x-2
2. (1/2)^2x = 32 + (1/2)^x-2
1. (1/3)^2x = 162 - (1/3)^x-2
2. (1/2)^2x = 32 + (1/2)^x-2
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1. (1/3)²ˣ = 162 - (1/3)ˣ-2Замена переменной:
(1/3)ˣ=t; t>0
t²+(1/3)⁻²·t -162=0
t²+9t-162=0
D=81+4·162=81·(1+8)=81·9=(9·3)²=27²
t=(-9-27)/2=-18 <0 не удовл условию t>0 или
t=(-9+27)/2=9
(1/3)ˣ=9
x=-2
О т в е т. -2.
2. (1/2)²ˣ = 32 + (1/2)ˣ-2
Замена переменной:
(1/2)ˣ=t; t>0
t²-(1/2)⁻²·t -32=0
t²-4t-32=0
D=16+4·32=16·(1+8)=16·9=(4·3)²=12²
t=(4-12)/2=-4 <0 не удовл условию t>0 или
t=(4+12)/2=8
(1/2)ˣ=8
x=-3
О т в е т. -3.