Exercise ID199

Algebra → Quadratic equations, inequalities and systems of equations → Equations Reducible to Quadratic Form
[Level: ] [Number of helps: 1] [Number of pictures: 0] [Number of steps: 37] [Number of characters: 0]

Solve the following equation.

2x5+x4-19x3+19x2-x-2=0

2x5+x4-19x3+19x2-x-2=0 x1=1 2x5+1x4-19x3+19x2-1x-2=0 21-1919-1-2--------------123-16320 x-1(2x4+3x3-16x2+3x+2)=0 2x4+3x3-16x2+3x+2=0 2x4+3x3-16x2+3x+2=0 ·1x2 2x4x2+3x3x2-16x2x2+3xx2+2x2=0 2x2+3x-16+3x+2x2=0 2x2+2x2+3x+3x-16=0 2x2+1x2+3x+1x-16=0 t=x+1x t2=x+1x2=x2+1x2=x4+2x2+1x2=x4x2+2x2x2+1x2=x2+2+1x2 t2-2=x2-1x2 2t2-2+3t-16=0 2t2-4+3t-16=0 2t2+3t-20=0 2t2+3t-20=0  a=2 ; b=3 ; c=-20 t1,2=-3±33-4·2·-202·2=-3±9+1604=-3±134 t1=-3+134=104=52 ; t2=-3-134=-164=-4 t1=52 ; t2=-4 t1=52  52=x+1x 52=x+1x ·2x 52·2x=x·2x+1x·2x 5x=2x2+2 2x2-5x+2=0 2x2-5x+2=0  a=2 ; b=-5 ; c=2 x2,3=5±52-4·2·22·2=5±25-164=5±94=5±34 x2=5+34=84 ; x3=5-34=24 x2=2  ;  x3=12 t2=-4 -4=x+1x -4=x+1x·x -4·x=x·x+1x·x -4x=x2+1 x2+4x+1=0 x2+4x+1=0 a=1 ; b=4 ; c=1 x4,5=-4±42-4·1·12·1=-4±16-42=4±122=4±4·32=4±4·32=4±232=22±32=2±3 x4=2+3 ; x5=2-3 x1=1 ; x2=2 ; x3=-12 ; x4=-2+3 ; x5=-2-3
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x1=1 ; x2=2 ; x3=-12 ; x4=-2+3 ; x5=-2-3
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