help (x+1)^(1/2) +(x^2 −1)^(1/3) =4 find x


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Question Number 62045 by hovea cw last updated on 14/Jun/19

$help$ ${(x + 1)}^{1 / 2} + {(x^{2} - 1)}^{1 / 3} = 4$ $find x$
	Answered by MJS last updated on 14/Jun/19

	${(x + 1)}^{1 / 2} + {(x^{2} - 1)}^{1 / 3} = 4$ ${(x^{2} - 1)}^{1 / 3} = 4 - {(x + 1)}^{1 / 2}$ $both sides^{3}$ $x^{2} - 1 = 12 x + 76 - (x + 49) \sqrt{x + 1}$ $77 + 12 x - x^{2} = (x + 49) \sqrt{x + 1}$ $both sides^{2} [we will get some false solutions]$ $x^{4} - 25 x^{3} - 109 x^{2} - 651 x + 3528 = 0$ $trying factors if 3528 \Rightarrow x_{1} = 3$ $looking at the graph of f (x) = {(x + 1)}^{1 / 2} + {(x^{2} - 1)}^{1 / 3} - 4$ $we see {it}^{'} s the only real solution$ $if you need complex solutions you must solve$ $(x - 3) (x^{3} - 22 x^{2} - 175 x - 1176) = 0$ $using {Cardano}^{'} s formula$
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