Check whether the following are Quadratic equations
${(x + 2)}^{3} = 2 x (x^{2} - 1)$

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Solution

${(x + 2)}^{3} = 2 x (x^{2} - 1)$
$\Rightarrow x^{3} + 8 + 6 x (x + 2) = 2 x^{3} - 2 x$
$\Rightarrow x^{3} + 8 + 6 x^{2} + 12 x - 2 x^{3} + 2 x = 0$
$\Rightarrow - x^{3} + 4 x^{2} + 14 x + 8 = 0$ has its highest power $3$
Hence it is not a quadratic equation.

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Similar questions

Q. Check whether the following is quadratic equation.

(x + 2)^{3} = 2 x (x^{2} - 1)

Q. Question 1(vii)
Check whether the following are quadratic equations:
(vii)

(x + 2)^{3} = 2 x (x^{2} - 1)

Q. Simplify

(x + 2)^{3} = 2 x (x^{2} - 1)

and check whether its is a quadratic equation.

Q. Check whether the following equations are quadratic?

x + \frac{1}{x} + x^{2}, x \neq 0

Check whether the following are quadratic equations :
(i) ${(x + 1)}^{2} = 2 (x - 3)$
(ii) $x^{2} - 2 x = (- 2) (3 - x)$
(iii) $(x - 2) (x + 1) = (x - 1) (x + 3)$
(iv) $(x - 3) (2 x + 1) = x (x + 5)$
(v) $(2 x - 1) (x - 3) = (x + 5) (x - 1)$
(vi) $x^{2} + 3 x + 1 = {(x - 2)}^{2}$
(vii) ${(x + 2)}^{3} = 2 x (x^{2} - 1)$
(viii) $x^{3} - 4 x^{2} - x + 1 = {(x - 2)}^{3}$

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Check whether the following are Quadratic equations(x+2)3=2x(x2−1)

(x+2)3=2x(x2−1)⇒x3+8+6x(x+2)=2x3−2x⇒x3+8+6x2+12x−2x3+2x=0⇒−x3+4x2+14x+8=0 has its highest power 3Hence it is not a quadratic equation.

Check whether the following are Quadratic equations
${(x + 2)}^{3} = 2 x (x^{2} - 1)$

${(x + 2)}^{3} = 2 x (x^{2} - 1)$
$\Rightarrow x^{3} + 8 + 6 x (x + 2) = 2 x^{3} - 2 x$
$\Rightarrow x^{3} + 8 + 6 x^{2} + 12 x - 2 x^{3} + 2 x = 0$
$\Rightarrow - x^{3} + 4 x^{2} + 14 x + 8 = 0$ has its highest power $3$
Hence it is not a quadratic equation.