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Answer:

We know that the general form of quadratic equation is ax

2

+bx+c=0.

The given equation is (x+2)

3

=2x(x

2

−1) can be simplified as follows:

(x+2)

3

=2x(x

2

−1)

⇒x

3

+2

3

+(3×x×2)(x+2)=2x

3

−2x(∵(a+b)

3

=a

3

+b

3

+3ab(a+b))

⇒x

3

+8+6x(x+2)=2x

3

−2x

⇒x

3

+8+6x

2

+12x=2x

3

−2x

⇒x

3

+8+6x

2

+12x−2x

3

+2x=0

⇒−x

3

+6x

2

+14x+8=0

Since the variable x in the equation −x

3

+6x

2

+14x+8=0 has degree 3, therefore, it is not of the form ax

2

+bx+c=0.

Hence, the equation (x+2)

3

=2x(x

2

−1) is not a quadratic equation.

72

Hristina

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