(32m^2-32m)^2-4(4m^2+9)(64m^2+38)=0 పరిష్కరించండి

$$( 32 m ^ { 2 } - 32 m ) ^ { 2 } - 4 ( 4 m ^ { 2 } + 9 ) ( 64 m ^ { 2 } + 38 ) = 0$$

mని పరిష్కరించండి (సంకీర్ణ పరిష్కారం)

$$m=-\frac{\left(1+\sqrt{3}i\right)\left(-\sqrt{3}\sqrt[3]{288\sqrt{79077867}-2569283}i-\sqrt[3]{288\sqrt{79077867}-2569283}-59\sqrt{3}i+2\sqrt[3]{-288\sqrt{79077867}-2569283}+59\right)}{768}\approx 0.036730493-0.777937855i$$

$$m=\frac{\sqrt[3]{288\sqrt{79077867}-2569283}+\sqrt[3]{-288\sqrt{79077867}-2569283}-59}{192}\approx 0.194411198+0.868974852i$$

$$m=-\frac{\left(-\sqrt{3}i+1\right)\left(-\sqrt[3]{288\sqrt{79077867}-2569283}+2\sqrt[3]{-288\sqrt{79077867}-2569283}+59+\sqrt{3}\sqrt[3]{288\sqrt{79077867}-2569283}i+59\sqrt{3}i\right)}{768}\approx -1.153016691-0.091036997i$$

mని పరిష్కరించండి

$$m=\frac{-\sqrt[3]{288\sqrt{79077867}+2569283}-\sqrt[3]{2569283-288\sqrt{79077867}}-59}{192}\approx -1.310697396$$