1.(x2−1)(x2+5x+6)=0⇔[x2−1=0x2+5x+6=0⇔[x2=1(x+3)(x+2)=0⇔⎡⎢⎣x=±1[x=−3x=−22.(x2−6x)2−2(x−3)2=0⇔x4−12x3+36x2−2(x2−6x+9)=81⇔x4−12x3+36x2−2x2+12x−18=81⇔x4−3x3−9x3+342+12x−99=0⇔x4−3x3−9x3+27x2+7x2−2x+33x−99=0⇔x3(x−3)−9x2(x−3)+7x(x−3)+33(x−3)=0⇔(x−3)(x3−9x2+7x+33)=0⇔(x−3)(x3−3x2−6x2+18x−11x+33)=0⇔(x−3)[x2(x−3)−6x(x−3)−11(x−3)]=0⇔(x−3)2(x2−6x−11)=0⇔[(x−3)2=0x2−6x−11=0⇔⎡⎢⎣x−3=0x=−(−6)±√(−6)2−4×1×(−11)2×1⇔⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣x=3⎡⎢ ⎢ ⎢⎣x=6+4√52x=6−4√52⇔⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣x=3⎡⎢ ⎢ ⎢⎣x=2(3+2√5)2x=2(3−2√5)2⇔⎡⎢⎣x=3x=3+2√5x=3−2√53.x(x+1)(x+2)(x+3)=120⇔(x2+x)(x+2)(x+3)=120⇔(x3+3x2+2x)(x+3)=120⇔x4+6x3+11x+6x=120⇔x4−2x3+8x3−16x2+27x2−54x+60x−120=0⇔x3(x−2)+8x2(x−2)+27x(x−2)+60(x−2)=0⇔(x−2)(x3+8x2+27x+60)=0⇔(x−2)(x3+5x2+3x2+15x+12x+60)=0⇔(x−2)[x2(x+5)+3x(x+5)+12(x+5)]=0⇔(x−2)(x+5)(x2+3x+12)=0⇔⎡⎢⎣x−2=0x+5=0x2+3x+12=0⇔⎡⎢ ⎢ ⎢ ⎢⎣x=2x=−5x=−3±√32−4×1×122×1⇔⎡⎢ ⎢ ⎢⎣x=2x=−5x=−3±√−392(!)⇒x∉R4.x3+5x2−10x−8=0⇔(x−2)(x2+2x+4)+5x(x−2)=0⇔(x−2)(x2+2x+4+5x)=0⇔(x−2)(x2+7x+4)=0⇔[x−2=0x2+7x+4=0⇔⎡⎢⎣x=2x=−7±√72−4×1×42×1⇔⎡⎢⎣x=2x=−7±√332⇔⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣x=2x=−7+√332x=−7−√332
1.(x2−1)(x2+5x+6)=0⇔[x2−1=0x2+5x+6=0⇔[x2=1(x+3)(x+2)=0⇔⎡⎢⎣x=±1[x=−3x=−22.(x2−6x)2−2(x−3)2=0⇔x4−12x3+36x2−2(x2−6x+9)=81⇔x4−12x3+36x2−2x2+12x−18=81⇔x4−3x3−9x3+342+12x−99=0⇔x4−3x3−9x3+27x2+7x2−2x+33x−99=0⇔x3(x−3)−9x2(x−3)+7x(x−3)+33(x−3)=0⇔(x−3)(x3−9x2+7x+33)=0⇔(x−3)(x3−3x2−6x2+18x−11x+33)=0⇔(x−3)[x2(x−3)−6x(x−3)−11(x−3)]=0⇔(x−3)2(x2−6x−11)=0⇔[(x−3)2=0x2−6x−11=0⇔⎡⎢⎣x−3=0x=−(−6)±√(−6)2−4×1×(−11)2×1⇔⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣x=3⎡⎢ ⎢ ⎢⎣x=6+4√52x=6−4√52⇔⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣x=3⎡⎢ ⎢ ⎢⎣x=2(3+2√5)2x=2(3−2√5)2⇔⎡⎢⎣x=3x=3+2√5x=3−2√53.x(x+1)(x+2)(x+3)=120⇔(x2+x)(x+2)(x+3)=120⇔(x3+3x2+2x)(x+3)=120⇔x4+6x3+11x+6x=120⇔x4−2x3+8x3−16x2+27x2−54x+60x−120=0⇔x3(x−2)+8x2(x−2)+27x(x−2)+60(x−2)=0⇔(x−2)(x3+8x2+27x+60)=0⇔(x−2)(x3+5x2+3x2+15x+12x+60)=0⇔(x−2)[x2(x+5)+3x(x+5)+12(x+5)]=0⇔(x−2)(x+5)(x2+3x+12)=0⇔⎡⎢⎣x−2=0x+5=0x2+3x+12=0⇔⎡⎢ ⎢ ⎢ ⎢⎣x=2x=−5x=−3±√32−4×1×122×1⇔⎡⎢ ⎢ ⎢⎣x=2x=−5x=−3±√−392(!)⇒x∉R4.x3+5x2−10x−8=0⇔(x−2)(x2+2x+4)+5x(x−2)=0⇔(x−2)(x2+2x+4+5x)=0⇔(x−2)(x2+7x+4)=0⇔[x−2=0x2+7x+4=0⇔⎡⎢⎣x=2x=−7±√72−4×1×42×1⇔⎡⎢⎣x=2x=−7±√332⇔⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣x=2x=−7+√332x=−7−√332
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