حل (16x^3+9)=(2x+1)

$$( 16 x ^ { 3 } + 9 ) = ( 2 x + 1 )$$

برای x حل کنید (complex solution)

$$x=-\frac{36^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(-\sqrt{3}\sqrt[3]{\sqrt{5178}-72}i-\sqrt[3]{\sqrt{5178}-72}+2\sqrt[3]{-\sqrt{5178}-72}\right)}{288}\approx 0.344310196-0.687298496i$$

$$x=\frac{36^{\frac{2}{3}}\left(\sqrt[3]{\sqrt{5178}-72}+\sqrt[3]{-\sqrt{5178}-72}\right)}{72}\approx 0.42306286+0.732766368i$$

$$x=-\frac{36^{\frac{2}{3}}\left(-\sqrt{3}i+1\right)\left(-\sqrt[3]{\sqrt{5178}-72}+2\sqrt[3]{-\sqrt{5178}-72}+\sqrt{3}\sqrt[3]{\sqrt{5178}-72}i\right)}{288}\approx -0.767373055-0.045467872i$$

برای x حل کنید

$$x=-\frac{36^{\frac{2}{3}}\left(\sqrt[3]{\sqrt{5178}+72}+\sqrt[3]{72-\sqrt{5178}}\right)}{72}\approx -0.84612572$$