СРОЧНО 5*9^x+3*25^x=8*15^x

Question

СРОЧНО 5*9^x+3*25^x=8*15^x

Answer 1

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