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Question Number 48368 by behi83417@gmail.com last updated on 22/Nov/18

	Answered by MJS last updated on 22/Nov/18

	$a^{\frac{1}{3}} - b^{\frac{1}{3}} = c$ $a - 3 a^{\frac{2}{3}} b^{\frac{1}{3}} + 3 a^{\frac{1}{3}} b^{\frac{2}{3}} - b = c^{3}$ $- 3 a^{\frac{1}{3}} b^{\frac{1}{3}} (a^{\frac{1}{3}} - b^{\frac{1}{3}}) = - a + b + c^{3}$ $- 3 {c a}^{\frac{1}{3}} b^{\frac{1}{3}} = - a + b + c^{3}$ $- 27 {a b c}^{3} = {(- a + b + c^{3})}^{3}$ $- 1728 (21 x - 62) (21 x + 62) = - 216000$ $(21 x - 62) (21 x + 62) = 125$ $441 x^{2} - 3969 = 0$ $x^{2} = 9$ $x = \pm 3$
	Commented by behi83417@gmail.com last updated on 23/Nov/18

	$v e r y n i c e s o l u t i o n . t h a n k y o u v e r y m u c h .$
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