Question

(x^2)^x = (x^x)^x-3

tentukan nilai x​

Answer 1

[tex]( {x}^{2} ) {}^{x} = ( {x}^{x} ) {}^{x - 3} [/tex]

[tex] {\cancel x}^{2x} = {\cancel x}^{ {x}^{2} - 3x} [/tex]

[tex]2x = {x}^{2} - 3x [/tex]

[tex] {x}^{2} - 3x = 2x[/tex]

[tex] {x}^{2} - 3x - 2x = 0[/tex]

[tex] {x}^{2} - 5x = 0[/tex]

[tex]x(x - 5) = 0[/tex]

[tex] \\ [/tex]

[tex]x_1 = \frac{0}{x - 5} [/tex]

[tex]x_1 = \boxed{0}[/tex]

[tex] \\ [/tex]

[tex]x_2 - 5 = \frac{0}{x} [/tex]

[tex]x_2 - 5 = 0[/tex]

[tex]x_2 = \boxed{5}[/tex]

[tex] \\ [/tex]

[tex]\bf HP = \{ \: 0, \: 5 \: \}[/tex]