1. Find all real solutions to \(\[x^4 - 10x^2 + 9 = 0.\]\)
2. Find all real solutions to \(\[x^2+4x+4=100x^2+20x+1.\]\)
1. Let u = x2, so we have: u2 - 10u + 9 = 0
This factors as (u-1)*(u-9) = 0 so u = 1 or u = 9
Hence x2 = 1 or x2 = 9 so x = ±1 or x = ±3
2. Rearrange by collecting all terms on one side of the equation: 99x2 +16x - 3 = 0
Use the general equation for the solution of a quadratic: x = (-16 ±√[162 - 4*99*(-3)])/(2*99)