Which of the following is a quadratic equation?
(i) `x^(2)+2x+1=(4-x)^(2)+3` (ii) `-2x^(2)=(5-x)(2x-(2)/(5))`
(iii) `(k+1)x^(2)+(3)/(2)x=7" wherek"=-1` (iv) `x^(3)-x^(2)=(x-1)^(3)`

Explanation

(i) `x^(2)+2x+1=(4-x)+3`
`impliesx^(2)+2x+1=16+x^(2)-8x+3`
`implies10x-8=0` which is not in the form of `ax^(2)+bx+c,ane0`
Thus, the equation is not quadratic.
(ii) `-2x^(2)=(5-x)(2x-(2)/(5))`
`implies-2x^(2)=10x-2-2x^(2)+(2x)/(5)`
`implies50x+2x-10=0`
`implies52x-10=0`
which is not a quadratic equation.
(iii) `(k+1)x^(2)+(3)/(2)x=7`
Given k=-1
`implies(-1+1)x^(2)+(3)/(2)x=7`
`implies3x-14=0`
which is not a quadratic equation.
(iv) `x^(3)-x^(2)=(x-1)^(3)`
`impliesx^(3)-x^(2)=x^(3)-1-3x(x-1)" "[because(a-b)^(3)=a^(3)-b^(3)-3ab(a-b)]`
`impliesx^(3)-x^(2)=x^(3)-1-3x^(2)+3x`
`implies2x^(2)-3x+1=0`
which is in the form of `ax^(2)+bx+c=0,ane0`
Hence, it is a quadratic equation.