What are the solutions of the equation x4 – 9x2 + 8 = 0? Use u substitution to solve.

Answer:[tex](x ^ 2 -1)(x ^ 2 -8)\\\\x = 2\sqrt{2}\\\\x = - 2\sqrt{2}\\\\x = 1\\\\x = -1[/tex]Step-by-step explanation:We have the following equation [tex]x^4 - 9x2 + 8 = 0[/tex]To solve this problem, do:[tex]u = x ^ 2[/tex]then it has:[tex]u ^ 2 - 9u + 8 = 0[/tex]Then he has a second-degree equation.To resolve factor.You must find 2 numbers that when you add them get -9 and multiply them get 8.These numbers are:u = -1 and u = -8Then it has:[tex](u-1)(u-8) = 0[/tex][tex]u = 1[/tex]and[tex]u = 8[/tex]Remember that [tex]u = x ^ 2[/tex]Then it has:[tex](x ^ 2 -1)(x ^ 2 -8)\\\\x = 2\sqrt{2}\\\\x = - 2\sqrt{2}\\\\x = 1\\\\x = -1[/tex]