Check whether the following is a quadratic eq | vedclass

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(A) Given equation: $(x+2)^{3} = x^{3}-4$Expanding the left-hand side using the identity $(a+b)^{3} = a^{3}+b^{3}+3ab(a+b)$:$(x+2)^{3} = x^{3} + 2^{3}

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(A) Given equation: $(x+2)^{3} = x^{3}-4$Expanding the left-hand side using the identity $(a+b)^{3} = a^{3}+b^{3}+3ab(a+b)$:$(x+2)^{3} = x^{3} + 2^{3} + 3(x)(2)(x+2) = x^{3} + 8 + 6x(x+2) = x^{3} + 8 + 6x^{2} + 12x$Substituting this back into the equation:$x^{3} + 6x^{2} + 12x + 8 = x^{3} - 4$Subtracting $x^{3}$ from both sides:$6x^{2} + 12x + 8 = -4$Adding $4$ to both sides:$6x^{2} + 12x + 12 = 0$Dividing the entire equation by $6$:$x^{2} + 2x + 2 = 0$Since this equation is in the form $ax^{2} + bx + c = 0$ where $a 
eq 0$,it is a quadratic equation.

Check whether the following is a quadratic equation:
$(x+2)^{3} = x^{3}-4$

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Check whether the following is a quadratic equation:$(x+2)^{3} = x^{3}-4$

Similar Questions

Find the nature of the roots of the following quadratic equation. If real roots exist,find them:$2x^2 - 3x + 5 = 0$

Represent the following situation in the form of a quadratic equation:$A$ train travels a distance of $480 \, km$ at a uniform speed. If the speed had been $8 \, km/h$ less,then it would have taken $3 \, hours$ more to cover the same distance. We need to find the speed of the train.

Represent the following situation in the form of a quadratic equation:The product of two consecutive positive integers is $306$. We need to find the integers.

Check whether the following is a quadratic equation:$x^{2}-2x=(-2)(3-x)$

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