The equation x^3 + 8y^3 + 24xy = 64 represent | vedclass

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(C) The given equation is $x^3 + (2y)^3 + (-4)^3 - 3(x)(2y)(-4) = 0$.Using the algebraic identity $a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^

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One straight line and one point

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(C) The given equation is $x^3 + (2y)^3 + (-4)^3 - 3(x)(2y)(-4) = 0$.Using the algebraic identity $a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca) = 0$,we have:$(x + 2y - 4)(x^2 + 4y^2 + 16 - 2xy + 8y + 4x) = 0$.This implies $x + 2y - 4 = 0$ or $x^2 + 4y^2 - 2xy + 4x + 8y + 16 = 0$.The equation $x + 2y - 4 = 0$ represents a straight line.The second part $x^2 - 2xy + 4y^2 + 4x + 8y + 16 = 0$ can be written as $\frac{1}{2}[(x-y)^2 + (x+2)^2 + (2y+2)^2 + 8] = 0$,which represents a single point $(-4, -2)$.

The equation $x^3 + 8y^3 + 24xy = 64$ represents:

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