Subjective Type

Solve the following equation: $$x^{3} - 18x = 35$$.

Solution

Given equation, $$x^3-18x-35=0$$

$$\implies x^3 + 5x^2 - 5x^2 + 7x -25x - 35 = 0 \implies (x-5)(x^2+5x+7) = 0 $$

Solving the quadratic equation, we have $$x = \dfrac{-5\pm\sqrt{3}i}{2}$$

$$\therefore\,\,$$ roots of the given equation are $$x = 5, \dfrac{-5\pm\sqrt{3}i}{2}$$

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