Toán Lớp 8: Tìm x sao cho a) x²+5x+12 chia hết cho x-1 b) 2x²-7x+9 chia hết cho 2x-1

Question

Toán Lớp 8:  Tìm x sao cho a) x²+5x+12 chia hết cho x-1 b) 2x²-7x+9 chia hết cho 2x-1

haianhtu97 · Answer

$  $    Giải đáp + giải th&iacute;ch c&aacute;c bước giải :    a,   x^2+5x+12  vdots x-1   => x^2 - x + 6x - 6 + 18  vdots x-1   => x (x-1) + 6 (x-1)+18  vdots x-1   =>(x-1)(x+6) + 18  vdots x-1   Nhận x&eacute;t : x-1 vdots x-1   => (x-1)(x+6)  vdots x-1   => 18  vdots x-1   =>x-1 &isin;Ư (18)={1;-1;2;-2;3;-3;6;-6;9;-9;18;-18}   => x&isin;{2;0;3;-1;4;-2;7;-5;10;-8;18;-17}   Vậy x&isin;{2;0;3;-1;4;-2;7;-5;10;-8;18;-17} để x^2+5x+12 vdots x-1   b,   2x^2 - 7x+9  vdots 2x-1   =>2x^2-x - 6x + 3 + 6 vdots 2x-1   =>x(2x-1) - 3 (2x-1) + 6 vdots 2x-1   => (2x-1)(x-3)+6 vdots 2x-1   Nhận x&eacute;t : 2x-1 vdots 2x-1   => (2x-1)(x-3) vdots 2x-1   => 6 vdot 2x-1   =>2x-1 &isin; Ư (6)={1;-1;2;-2;3;-3;6;-6}   =>2x &isin; {2;0;3;-1;4;-2;7;-5}   =>x &isin; {1;0;3/2;(-1)/2;2;-1;7/2;(-5)/2}   Vậy x &isin; {1; 0; 3/2;(-1)/2;2;-1;7/2;(-5)/2} để 2x^2-7x+9 vdots 2x-1

diepbich93 · Answer

Giải đáp:   $ begin{array}{l} a){x^2} + 5x + 12    = {x^2} - x + 6x - 6 + 18    = x left( {x - 1}  right) + 6 left( {x - 1}  right) + 18    =  left( {x - 1}  right) left( {x + 6}  right) + 18   Do: left( {x - 1}  right) left( {x + 6}  right)  vdots  left( {x - 1}  right)     Leftrightarrow 18  vdots  left( {x - 1}  right)     Leftrightarrow  left( {x - 1}  right)  in  left {  begin{array}{l}  - 18; - 9; - 6; - 3; - 2; - 1;   1;2;3;6;9;18  end{array}  right }     Leftrightarrow x  in  left { { - 17; - 8; - 5; - 2; - 1;0;2;3;4;7;10;19}  right }   Vậy ,x  in  left { { - 17; - 8; - 5; - 2; - 1;0;2;3;4;7;10;19}  right }   b)   2{x^2} - 7x + 9    = 2{x^2} - x - 6x + 3 + 6    = x. left( {2x - 1}  right) - 3. left( {2x - 1}  right) + 6    =  left( {2x - 1}  right) left( {x - 3}  right) + 6    left( {2x - 1}  right) left( {x - 3}  right)  vdots  left( {2x - 1}  right)     Leftrightarrow 6  vdots  left( {2x - 1}  right)     Leftrightarrow  left( {2x - 1}  right)  in  left { { - 6; - 3; - 2; - 1;1;2;3;6}  right }     Leftrightarrow 2x  in  left { { - 5; - 2; - 1;0;2;3;4;7}  right }     Leftrightarrow x  in  left { { -  dfrac{5}{2}; - 1; -  dfrac{1}{2};0;1; dfrac{3}{2};2; dfrac{7}{2}}  right }   Vậy ,x  in  left { { -  dfrac{5}{2}; - 1; -  dfrac{1}{2};0;1; dfrac{3}{2};2; dfrac{7}{2}}  right }  end{array}$