Realizar esta ecuacion U ^ 4 + 8 = 0 , por el método de completar cuadrados?
Realizar esta ecuacion U ^ 4 + 8 = 0 , por el método de completar cuadrados. Con procedimiento gracias.
En resumen
<img src="https://tex.z-dn.net/?
Mejor respuesta
<img src="https://tex.z-dn.net/?f=u%5E4%2B8%3D0%5C%5C%5C%5C%0Au%5E4%2B2%5Ccdot2%5Csqrt2u%5E2%2B8-2%5Ccdot2%5Csqrt2u%5E2%3D0%5C%5C%5C%5C%0A%28u%5E2%2B2%5Csqrt2%29%5E2-4%5Csqrt2u%5E2%3D0%5C%5C%5C%5C%0A%28u%5E2-2%5Csqrt%5B4%5D2u%2B2%5Csqrt2%29%28u%5E2%2B2%5Csqrt%5B4%5D2u%2B2%5Csqrt2%29%3D0%5C%5C%5C%5C%28i%29~u%5E2-2%5Csqrt%5B4%5D2u%2B2%5Csqrt2%3D0~~o~~%28ii%29~u%5E2%2B2%5Csqrt%5B4%5D2u%2B2%5Csqrt2%3D0" />
<img src="https://tex.z-dn.net/?f=%28i%29~u%5E2-2%5Csqrt%5B4%5D2u%2B2%5Csqrt2%3D0%5C%5C%5C%5C%0A%5CDelta%3Db%5E2-4ac%5C%5C%5C%5C%0A%5CDelta%3D%28-2%5Csqrt%5B4%5D%7B2%7D%29%5E2-4%5Ccdot1%5Ccdot2%5Csqrt2%5C%5C%5C%5C%0A%5CDelta%3D4%5Csqrt2-8%5Csqrt2%5C%5C%5C%5C%0A%5CDelta%3D-4%5Csqrt2%5C%5C%5C%5C%5C%5C%0Au%3D%5Cdfrac%7B-b%5Cpm%5Csqrt%5CDelta%7D%7B2a%7D%3D%5Cdfrac%7B-%28-2%5Csqrt%5B4%5D2%29%5Cpm%5Csqrt%7B-4%5Csqrt2%7D%7D%7B2%5Ccdot1%7D%3D%5Cdfrac%7B2%5Csqrt%5B4%5D2%5Cpm2%5Csqrt%5B4%5D2i%7D%7B2%7D%5C%5C%5C%5C%0A%5Cboxed%7Bu%3D%5Csqrt%5B4%5D2%281%5Cpm%20i%29%7D" />
<img src="https://tex.z-dn.net/?f=%28ii%29~u%5E2%2B2%5Csqrt%5B4%5D2u%2B2%5Csqrt2%3D0%5C%5C%5C%5C%20%5CDelta%3Db%5E2-4ac%5C%5C%5C%5C%20%5CDelta%3D%282%5Csqrt%5B4%5D%7B2%7D%29%5E2-4%5Ccdot1%5Ccdot2%5Csqrt2%5C%5C%5C%5C%20%5CDelta%3D4%5Csqrt2-8%5Csqrt2%5C%5C%5C%5C%20%5CDelta%3D-4%5Csqrt2%5C%5C%5C%5C%5C%5C%20u%3D%5Cdfrac%7B-b%5Cpm%5Csqrt%5CDelta%7D%7B2a%7D%3D%5Cdfrac%7B-%282%5Csqrt%5B4%5D2%29%5Cpm%5Csqrt%7B-4%5Csqrt2%7D%7D%7B2%5Ccdot1%7D%3D%5Cdfrac%7B-2%5Csqrt%5B4%5D2%5Cpm2%5Csqrt%5B4%5D2i%7D%7B2%7D%5C%5C%5C%5C%20%5Cboxed%7Bu%3D%5Csqrt%5B4%5D2%28-1%5Cpm%20i%29%7D" />
Por lo tanto, las soluciones son :
<img src="https://tex.z-dn.net/?f=S%3D%5C%7B%5Csqrt%5B4%5D2%28-1-%20i%29%2C%5Csqrt%5B4%5D2%28-1%2Bi%29%2C%5Csqrt%5B4%5D2%281-i%29%2C%5Csqrt%5B4%5D2%281%2Bi%29%5C%7D" />.