1.

Check whether the following are quadratic equations : (i) `(x-2)^2+1=2x-3` (ii) `x(x+1)+8=(x+2)(x 2)`(iii) `x(2x+3)=x^2+1` (iv) `(x+2)^3=x^3-4`

Answer» (i) `(x-2)^2+1 = 2x-3`
`=>x^2+4-4x+1 = 2x-3`
`=>x^2-6x+8 = 0`
As coefficient of `x^2` is not `0`, so it is a quadratic equation.

(ii)`x(x+1)+8 = (x+2)(x-2)`
`=>x^2+x+8 = x^2-4`
`=>x+12 = 0`
As coefficient of `x^2` is `0`, so it is not a quadratic equation.

(iii) `x(2x+3) = x^2+1`
`=>2x^2+3x = x^2+1`
`=>x^2+3x-1 = 0`
As coefficient of `x^2` is not `0`, so it is a quadratic equation.

(iv) `(x+2)^3 = x^3-4`
`=>x^3+2^3+3(2)(x)(x+2) = x^3-4`
`=>x^3+8+6x^2+12x = x^3-4`
`=>6x^2+12x+12 = 0`
`=>x^2+2x+2 = 0`
As coefficient of `x^2` is not `0`, so it is a quadratic equation.


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