Toán Lớp 8: 5x(x-1)=x-1 -4(x-1)^2+(2x-1)(2x+1)=-3

Question

Toán Lớp 8:  5x(x-1)=x-1 -4(x-1)^2+(2x-1)(2x+1)=-3

baoquyen · Answer

$5x(x-1) =x-1$   $(=) 5x^2 -5x=x-1$   $(=) 5x^2 -5x-x+1=0$   $(=) 5x^2 -6x+1=0$   $(=) 5x^2 -x-5x+1=0$   $(=) x(5x-1)-(5x-1)=0$   $(=) (5x-1)(x-1)=0$   $(=) 5x-1=0$ hoặc $x-1=0$   $=) x=1/5$ hoặc $x=1$   _____________________   $-4(x-1)^2+(2x-1)(2x+1)=-3$   $(=) -4(x^2-2x+1) + 4x^2 -1=-3$   $(=) -4x^2 + 8x-4+4x^2 -1=-3$   $(=) 8x-5=-3$   $(=) 8x=-3+5$   $(=) 8x=2$   $=) x=1/4$

tuyetanhthu · Answer

Giải đáp:      ( begin{array}{l} a,    left[  begin{array}{l} x = 1   x =  dfrac{1}{5}  end{array}  right.   b,   x =  dfrac{1}{4}  end{array} )     Lời giải và giải thích chi tiết:      Ta c&oacute;:    ( begin{array}{l} a,   5x left( {x - 1}  right) = x - 1     Leftrightarrow 5x left( {x - 1}  right) -  left( {x - 1}  right) = 0     Leftrightarrow  left( {x - 1}  right) left( {5x - 1}  right) = 0     Leftrightarrow  left[  begin{array}{l} x - 1 = 0   5x - 1 = 0  end{array}  right.  Leftrightarrow  left[  begin{array}{l} x = 1   x =  dfrac{1}{5}  end{array}  right.   b,    - 4{ left( {x - 1}  right)^2} +  left( {2x - 1}  right) left( {2x + 1}  right) =  - 3     Leftrightarrow  - 4. left( {{x^2} - 2.x.1 + {1^2}}  right) +  left[ {{{ left( {2x}  right)}^2} - {1^2}}  right] =  - 3     Leftrightarrow  - 4. left( {{x^2} - 2x + 1}  right) +  left( {4{x^2} - 1}  right) =  - 3     Leftrightarrow  - 4{x^2} + 8x - 4 + 4{x^2} - 1 + 3 = 0     Leftrightarrow 8x - 2 = 0     Leftrightarrow x =  dfrac{1}{4}  end{array} )