5*9ˣ+3*25ˣ=8*15ˣ
5*9ˣ/ 15^x +3*25ˣ/15ˣ=8*15ˣ/15ˣ
5(3/5)ˣ+3(5/3)ˣ=8
5(3/5)ˣ* (3/5)ˣ+3(5/3)ˣ*(3*5)ˣ=8*(3/5)ˣ
5(3/5)²ˣ+3*1ˣ=8*(3/5)ˣ
замена (3/5)ˣ=а ОДЗ а>0
5а²-8а+3=0
D=64-60=4
a₁=(8+2)/10=1 (3/5)ˣ=1 x₁=0
a₂=(8-2)/10=3/5 (3/5)ˣ= 3/5 x₂=1
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5*9ˣ+3*25ˣ=8*15ˣ
5*9ˣ/ 15^x +3*25ˣ/15ˣ=8*15ˣ/15ˣ
5(3/5)ˣ+3(5/3)ˣ=8
5(3/5)ˣ* (3/5)ˣ+3(5/3)ˣ*(3*5)ˣ=8*(3/5)ˣ
5(3/5)²ˣ+3*1ˣ=8*(3/5)ˣ
замена (3/5)ˣ=а ОДЗ а>0
5а²-8а+3=0
D=64-60=4
a₁=(8+2)/10=1 (3/5)ˣ=1 x₁=0
a₂=(8-2)/10=3/5 (3/5)ˣ= 3/5 x₂=1