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1. Find all real solutions to \(\[x^4 - 10x^2 + 9 = 0.\]\)

2. Find all real solutions to \(\[x^2+4x+4=100x^2+20x+1.\]\)

 Mar 15, 2020
edited by Guest  Mar 15, 2020
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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)

 Mar 15, 2020

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