Toán Lớp 8: giải phương trình: $(x-1)^{2}=2(x^{2}-1)$

Question

Toán Lớp 8:  giải phương trình:  $(x-1)^{2}=2(x^{2}-1)$

bichhhathu · Answer

$ left(x-1 right)^2=2 left(x^2-1 right)$   $&rArr;x^2-2x+1=2x^2-2$   $&rArr;x^2-2x+1+2=2x^2-2+2$   $&rArr;x^2-2x+3=2x^2$   $&rArr;x^2-2x+3-2x^2=2x^2-2x^2$   $&rArr;-x^2-2x+3=0$   $&rArr;x_{1, :2}= dfrac{- left(-2 right) pm  sqrt{ left(-2 right)^2-4 left(-1 right) cdot  :3}}{2 left(-1 right)}$   $&rArr;x_{1, :2}= dfrac{- left(-2 right) pm  :4}{2 left(-1 right)}$    (&rArr; left[  begin{array}{l}x_1= dfrac{- left(-2 right)+4}{2 left(-1 right)}  x_2= dfrac{- left(-2 right)-4}{2 left(-1 right)} end{array}  right. )   (&rArr; left[  begin{array}{l}x=-3  x=1 end{array}  right. )    $ text{Vậy pt c&oacute; nghiệm {-3;1}}$

truongankimtrong · Answer

#Hugg   (x-1)^2=2(x^2-1)   &hArr;x^2-2x+1=2x^2-2   &hArr;x&sup2;-2x+1-2x^2+2=0   &hArr;-x^2-2x+3=0   &hArr;-x^2+x-3x+3=0   &hArr;-x(x-1)-3(x-1)=0   &hArr;(x-1)(-x-3)=0   1)  x-1=0&hArr;x=1   2)  -x-3=0&hArr;x=-3   Vậy S={1;-3}