(i)LHS=(x-2)2+1=x2-x+4+1=x2-x+
Therefore,(x-2)2+1=2x-3 can be written as
x2-x+=2x-3
x2-x+=0
It is in the form of ax2+bx+c=0.
Therefore the given equation is quadratic equation.
(ii)Here LHS=x(x+1)+8 = x2++8
RHS=(x+2)(x-2)=x2 - 4
Therefore, x2+x+8=x2-
x2++8-x2+=0
+ = 0
It is not in the form of ax2+bx+c=0.
therefore the given equation is not a quadratic equation.
(iii) Here,LHS=x(2x+3)=x2+x
So,x(2x+3)=x2+ can be written as
x2+x=x2+
Therefore,we get x2+x-=0.
So,the given equation is a quadratic equation.
(iv)Here,LHS=(x+2)3
=(x+2)2(x+2)
=(x2+4x+4)(x+2)
=x3+2x2+x2+x+4x+8
=x3+x2+x+8
Therefore,(x+2)3=x3-4 can be written as
x3+x2+x+8=x3- 4
x2+x+12=0 (or) x2+2x+2=0
It is in the form of ax2+bx+c=0.
So this equation is a qudratic equation.