Tentukan nilai x yg memenuhi persamaan 9^(x²+3x-1)+9^x²+3x=20-10(3^x²-3x)

jawab

9^(x²+3x -1) + 9^(x²+3x)  = 20 - 10 (3)^(x² - 3x)

misal x²+3x = a
9ᵃ⁺¹ + 9ᵃ  = 20 - 10. 3ᵃ
9. 9ᵃ + 9ᵃ + 10.3ᵃ = 20
10. 9ᵃ +10. 3ᵃ  =20
10 ( 9ᵃ + 3ᵃ) = 20
9ᵃ + 3ᵃ = 2
(3ᵃ)² +(3ᵃ) - 2 = 0

3ᵃ = b
b² + b - 2 =0
(b +2)(b -1)=0
b = -2  atau b = 1

b = -2 → 3ᵃ = -2 (TM)
b= 1 → 3ᵃ = 1 → a = 0

x²+ 3x = a = 0
x(x + 3)=0
x =  0 atau x = - 3