Ada yg bisa? (x - 5)^{3x²+4x+3} = (x - 5)^{x²+x-5}

[tex] (x - 5)^{3x^2+4x+3} = (x - 5)^{x^2+x-5}[/tex]
Berbentuk
[tex]h(x)^{f(x)}=h(x)^{g(x)} [/tex]

Split into 4 possibilities

[1.]
x - 5 = 0
x = 5

Subtitusi ke f(x) dan g(x)
∴ 3(5)² + 4(5) + 3 > 0 [memenuhi]
∴ (5)² + 5 - 5 > 0 [memenuhi]

[2.]
x - 5 = 1
x = 6

[3.]
x - 5 = -1
x = 4

Subtitusi ke f(x) dan g(x)
∴ 3(4)² + 4(4) + 3 = 67[ganjil]
∴ (4)² + 4 - 5 =15[ganjil]

[4.]
3x²+4x+3 = x² + x - 5
2x² + 3x + 8 = 0

>a = 2 , b = 3 , c = 8<

D = b² - 4ac
=>3² - 4(2)(8)
=>-55 < 0
x ∉ R

HP : { 5 , 6 , 4 }