Subjective Type

Solve the following equation: $$x^{3} + 72x - 1720 = 0$$.

Solution

Given equation, $$x^3+72x-1720=0$$

$$\implies x^3 + 10x^2 - 10x^2 + 172x -100x - 1720 = 0 \implies (x-10)(x^2+10x+172) = 0 $$

Solving the quadratic equation, we have $$x = -5\pm7\sqrt{3}i$$

$$\therefore\,\,$$ roots of the given equation are $$x = 10, -5\pm7\sqrt{3}i $$

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