Toán Lớp 8: x^2+4x=21 (x-2)^2- 9(x+1)^2=0 gấp

Question

Toán Lớp 8:  x^2+4x=21 (x-2)^2- 9(x+1)^2=0 gấp

cattien · Answer

Giải đáp:     $ begin{array}{l}x^2+4x=21   leftrightarrow x^2+4x-21=0   leftrightarrow x^2+7x-3x-21=0   leftrightarrow x(x+7)-3(x+7)=0   leftrightarrow (x+7)(x-3)=0   leftrightarrow  left[ begin{array}{l}x+7=0  x-3=0 end{array} right.   leftrightarrow  left[ begin{array}{l}x=-7  x=3 end{array} right.   text{Vậy}  S= {-7;3 }    (x-2)^2-9(x+1)^2=0   leftrightarrow (x-2)^2-(3(x+1))^2=0   leftrightarrow (x-2-3(x+1))(x-2+3(x+1))=0   leftrightarrow (x-2-3x-3)(x-2+3x+3)=0   leftrightarrow (-2x-5)(4x+1)=0   leftrightarrow  left[ begin{array}{l}-2x-5=0  4x+1=0 end{array} right.   leftrightarrow  left[ begin{array}{l}x=- dfrac{5}{2}  x=- dfrac{1}{4} end{array} right.   text{Vậy}   S= left {{- dfrac{1}{4};- dfrac{5}{2}} right } end{array}$

doanthulan · Answer

a) x^2+4x=21   &hArr;x^2+4x-21=0   &hArr;(x^2-3x)+(7x-21)=0   &hArr;x(x-3)+7(x-3)=0   &hArr;(x-3)(x+7)=0   &hArr; ( left[  begin{array}{l}x-3=0  x+7=0 end{array}  right. )    &hArr; ( left[  begin{array}{l}x=3  x=-7 end{array}  right. )    Vậy S={3,-7}   b) (x-2)^2-9(x+1)^2=0   &hArr;[x-2-3(x+1)][x-2+3(x+1)]=0   &hArr;(x-2-3x-3)(x-2+3x+3)=0   &hArr;(-2x-5)(4x+1)=0   &hArr; ( left[  begin{array}{l}-2x-5=0  4x+1=0 end{array}  right. )    &hArr; ( left[  begin{array}{l}x=- dfrac{5}{2}  x=- dfrac{1}{4} end{array}  right. )    Vậy S={-5/2,-1/4}