simplify : (x+b)^2x(2+3)^2=1
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MATHS
Simplify (x+2)
3
=2x(x
2
−1) and check whether its is a quadratic equation.
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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.
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 +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