解方程:x 4 -15x 2 +10x+24=0.
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x 4 -15x 2 +10x+24=0,
x 4 -16x 2 +x 2 +10x+24=0,
(x 4 -16x 2 )+(x 2 +10x+24)=0,
x 2 (x 2 -16)+(x+4)(x+6)=0,
x 2 (x+4)(x-4)+(x+4)(x+6)=0,
(x+4)(x 3 -4x 2 +x+6)=0,
(x+4)(x 3 -4x 2 +4x-3x+6)=0,
(x+4)[x(x-2) 2 -3(x-2)]=0,
(x+4)(x-2)(x 2 -2x-3)=0,
(x+4)(x-2)(x+1)(x-3)=0,
解得x 1 =-4,x 2 =-1,x 3 =2,x 4 =3.
x 4 -16x 2 +x 2 +10x+24=0,
(x 4 -16x 2 )+(x 2 +10x+24)=0,
x 2 (x 2 -16)+(x+4)(x+6)=0,
x 2 (x+4)(x-4)+(x+4)(x+6)=0,
(x+4)(x 3 -4x 2 +x+6)=0,
(x+4)(x 3 -4x 2 +4x-3x+6)=0,
(x+4)[x(x-2) 2 -3(x-2)]=0,
(x+4)(x-2)(x 2 -2x-3)=0,
(x+4)(x-2)(x+1)(x-3)=0,
解得x 1 =-4,x 2 =-1,x 3 =2,x 4 =3.
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