(i)Given (x+1)2=2(x-3)
x2+x+=2(x-3)=2x-6
x2+x+-2x+6=0
x2+=0 is a quadratic equation.
(ii)x2-2x=(-2)(3-x)
x2-2x=-2(3-x)
x2-2x=-6+2x
x2-x+=0 is a quadratic equation.
(iii)(x-2)(x+1)=(x-1)(x+3)
x(x+1)-2(x+1)
x(x+3)-1(x+3)
x2+x-2x-2=x2+3x-x-3
x2-x-2=x2+2x-3
x-=0 is not a quadratic equation.
(iv)(x-3)(2x+1)=x(x+5)
x(2x+1)-3(2x+1)=x.x+5.x
2x2+x-6x-3=x2+5x
2x2-5x-3-x2-5x=0
x2-x-=0 is a quadratic equation.
(v)(2x-1)(x-3)=(x+5)(x-1)
2x(x-3)-1(x-3)=x(x-1)+5(x-1)
2x2-6x-x+3=x2-x+5x-5
2x2-7x+3-x2-4x+5=0
x2-x+=0
Hence its a quadratic equation.
(vi)x2+3x+1=(x-2)2
x2+3x+1=x2-4x+4
x-3=0 is not a quadratic equation.
(vii)(x+2)3=2x(x2-1)
x3+6x2+12x+8=2x3-2x
[∵(a+b)3=a3+3a2b+3ab2+b3]
-x3+x2+x+8=0
It is not a quadratic equation.
(viii)x3-4x2-x+1=(x-2)3
x3-4x2-x+1=x3-6x2+12x-8
6x2-12x+8-4x2-x+1=0
2x2-x+=0 is a quadratic equation.