3^x+ 3^5-x = 36 ..tolong bantu jawab ya kak :)

jawab

3ˣ + 3⁵⁻ˣ = 36
3ˣ + 3⁵.3⁻ˣ = 36

misalkan 3ˣ = a

a + 243/a = 36....kalikan a
a² + 243 = 36a
a² - 36 a + 243 = 0
(a - 27)(a - 9) = 0
a = 27  atau a = 9

3ˣ = a
a= 27  → 3ˣ = 27 = 3³
x = 3

a= 9  → 3ˣ = 9 = 3²
x  = 2

HP x = (2, 3)

3ˣ + 3⁵⁻ˣ = 36
3ˣ + 3⁵ . 3⁻ˣ = 36  (kalikan dengan 3ˣ)
3²ˣ + 3⁵ = 36 . 3ˣ
3²ˣ - 36. 3ˣ + 243 = 0

misalkan
y = 3ˣ , maka
y² - 36y + 243 = 0
(y - 9)(y - 27) = 0
y = 9    y = 27

(i)
y = 9
3ˣ = 9
x = 2

(ii)
y = 27
3ˣ = 27
x = 3

jadi HP = {2 , 3}