itbealex
itbealex itbealex
  • 25-06-2022
  • Mathematics
contestada

What are the soultions of the equation x^4 - 9x^2 + 8 = 0? Use u substitution to solve.​

Respuesta :

culveryolanda46
culveryolanda46 culveryolanda46
  • 25-06-2022

Step-by-step explanation:

Let u=x^2.

Notice that

[tex] {x}^{4} - 9 {x}^{2} + 8 = 0[/tex]

[tex]( {x}^{2} ) {}^{2} - 9( {x}^{2} ) + 8 = 0[/tex]

[tex]u {}^{2} - 9u + 8 = 0[/tex]

[tex](u - 8)(u - 1) = 0[/tex]

[tex]u = 8[/tex]

[tex]u = 1[/tex]

Replace x^2= u

[tex] {x}^{2} = 8[/tex]

[tex]x = ±2 \sqrt{2} [/tex]

[tex] {x}^{2} = 1[/tex]

[tex]x = ±1[/tex]

So our answer is

[tex]±1 \: [/tex]

and

[tex]±2 \sqrt{2} [/tex]

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