Toán Lớp 8: b1: tìm x a, (x-1) ³ -4x +4 =0 b, (x-2) ³ -x +2=0 c, (x-2) ³=100x-200

Question

Toán Lớp 8:  b1: tìm x a, (x-1) ³ -4x +4 =0 b, (x-2) ³ -x +2=0 c, (x-2) ³=100x-200

thanhthuythu · Answer

Giải đáp:    a,&hArr; (x-1)&sup3; -4(x-1)=0   &hArr;(x-1)((x-1)&sup2;-4)=0   &hArr; (x-1)(x-3)(x+1)=0   &hArr; x= -1 , 1 , 3   b, &hArr; (x-2)&sup3;-(x-2)=0   &hArr;(x-2)((x-2)&sup2;-1)=0   &hArr;(x-2)(x-3)(x-1)=0   &hArr;x= 1;2;3   c,&hArr;(x-2)&sup3;=100(x-2)   &hArr;(x-2)((x-2)&sup2;-100)=0   &hArr;(x-2)(x+8)(x-12)=0   &hArr;x= 2;-8;12

behocgioitoan · Answer

Giải đáp:   $a) (x-1)&sup3;-4x+4=0$   $&hArr; (x-1)&sup3;-4.(x-1)=0$   $&hArr; (x-1).[(x-1)&sup2;-2&sup2;]=0$   $&hArr; (x-1).(x-1-2).(x-1+2)=0$   $&hArr; (x-1).(x-3).(x+1)=0$   $&hArr;$  ( left[  begin{array}{l}x-1=0  x-3=0  x+1=0 end{array}  right. ) $&hArr;$   ( left[  begin{array}{l}x=1  x=3  x=-1 end{array}  right. )    $ text{Vậy x&isin; {&plusmn;1;3}}$   $b) (x-2)&sup3; -x+2=0$   $&hArr; (x-2)&sup3;- (x-2)=0$   $&hArr; (x-2).[(x-2)&sup2;-1&sup2;]=0$   $&hArr; (x-2-1).(x-2+1)=0$   $&hArr; (x-3).(x-1).(x-2)=0$   $&hArr;$  ( left[  begin{array}{l}x-3=0  x-1=0  x-2=0 end{array}  right. ) $&hArr;$   ( left[  begin{array}{l}x=3  x=1  x=2 end{array}  right. )    $ text{Vậy x &isin; {1;3;2}}$   $c) (x-2)&sup3;=100x-200$   $&hArr; (x-2)&sup3;= 100.(x-2)$   $&hArr; (x-2)&sup3;-100.(x-2)=0$   $&hArr; (x-2).[(x-2)&sup2;-10&sup2;]=0$   $&hArr; (x-2).(x-2-10).(x-2+10)=0$   $&hArr; (x-2).(x-12).(x+8)=0$   $&hArr;$  ( left[  begin{array}{l}x-2=0  x-12=0  x+8=0 end{array}  right. ) $&hArr;$   ( left[  begin{array}{l}x=2  x=12  x=-5 end{array}  right. )    $ text{Vậy x &isin; {2;12;-8}}$   $@Win$