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Question Number 187357 by cortano12 last updated on 16/Feb/23

	Answered by Humble last updated on 16/Feb/23

	$3 \sqrt{5} \sqrt{2 x + 3} + 2 \sqrt{5} \sqrt{3 x + 2} = \sqrt{3 x + 2} \sqrt{2 x + 3}$ $21600 x^{2} + 46800 x + 21600 = 36 x^{4} - 1644 x^{3} + 16741 x^{2} + 46306 x + 28561$ $36 x^{4} - 1644 x^{3} - 4859 x^{2} - 494 x + 6961 = 0$ $(x - 1) (36 x^{3} - 1608 x^{2} - 6467 x - 6961) = 0$ $x = 1 o r 36 x^{3} - 1608 x^{2} - 6467 x - 6961 = 0$ $b u t x \neq 1$ $36 x^{3} - 1608 x^{2} - 6467 x - 6961 = 0$ $A p p l y i n g N - R M e t h o d$ $x \approx 48.45625 . . .$
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