Ejercicio 282

Ejercicio 282

1. x 4 –1 =0 ( x 2 +1 ) ( x 2 –1 ) =0 ( x 2 +1 ) ( x+1 ) ( x–1 ) =0 x 1 +1 =0 x 1 =–1 x 2 –1 =0 x 2 =1 x 2 +1 =0 x 2 =–1 x = ± –1 x 3 =i x 4 =–i
2. x 3 +1 =0 ( x+1 ) ( x 2 –x+1 ) =0 x+1 =0 x 1 =–1 x 2 –x+1 =0 x = –( –1 ) ± ( –1 ) 2 –4( 1 ) ( 1 ) 2( 1 ) x = 1 ± 1–4 2 x = 1 ± –1 3 2 x = 1 ± 3 i 2 x 1 = 1+ 3 i 2 x 2 = 1– 3 i 2
3. x 4 =81 x 4 –81 =0 ( x 2 +9 ) ( x 2 –9 ) =0 ( x 2 +9 ) ( x–3 ) ( x+3 ) =0 x 1 –3 =0 x 1 =3 x 2 +3 =0 x 2 =–3 x 2 +9 =0 x 2 =–9 x = ± – 3 2 x = ± 3 –1 x 3 =3i x 4 =–3i
4. x 4 –256 =0 ( x 2 +16 ) ( x 2 –16 ) =0 ( x 2 +16 ) ( x–4 ) ( x+4 ) =0 x 1 –4 =0 x 1 =4 x 2 +4 =0 x 2 =–4 x 2 +16 =0 x 2 =–16 x = ± – 4 2 x = ± 4 –1 x 3 =4i x 4 =–4i
5. x 3 +8 =0 ( x+2 ) ( x 2 –2x+4 ) =0 x 1 +2 =0 x 1 =–2 x 2 –2x+4 =0 x = –( –2 ) ± ( –2 ) 2 –4( 1 ) ( 4 ) 2( 1 ) x = 2 ± 4–16 2 x = 2 ± –12 2 x = 2 ± ( –3 ) ( 2 2 ) 2 x = 2 ± 2 ( 3 ) ( –1 ) 2 x = 2 ( 1 ± 3 i ) 2 x 2 =1+ 3 i x 3 =1– 3 i
6. x 4 –625 =0 ( x 2 +25 ) ( x 2 –25 ) =0 ( x 2 +25 ) ( x–5 ) ( x+5 ) =0 x 1 –5 =0 x 1 =5 x 2 +5 =0 x 2 =–5 x 2 +25 =0 x 2 =–25 x = ± –25 x = ± ( –1 ) ( 5 2 ) x = ± 5i x 3 =5i x 4 =–5i
7. x 3 +64 =0 ( x+4 ) ( x 2 –4x+16 ) =0 x+4 =0 x 1 +4 =0 x 1 =–4 x 2 –4x+16 =0 x = –( –4 ) ± ( –4 ) 2 –4( 1 ) ( 16 ) 2( 1 ) x = 4 ± 16–64 2 x = 4 ± –48 2 x = 4 ± ( –3 ) ( 4 2 ) 2 x = 4 ± 4 3 –1 2 x = 2 ( 2 ± 2 3 i ) 2 x 2 =2+2 3 i x 3 =2–2 3 i
8. x 6 –729 =0 ( x 3 –27 ) ( x 3 +27 ) =0 ( x–3 ) ( x 2 +3x+9 ) ( x+3 ) ( x 2 –3x+9 ) =0 x 1 –3 =0 x 1 =3 x 2 +3 =0 x 2 =–3 x 2 +3x+9 =0 x = –3 ± 3 2 –4( 1 ) ( 9 ) 2( 1 ) x = –3 ± 9–36 2 x = –3 ± –27 2 x = –3 ± ( –1 ) ( 3 3 ) 2 x = –3 ± 3 3 –1 2 x = –3 ± 3 3 i 2 x 3 = –3–3 3 i 2 x 4 = –3+3 3 i 2 x 2 –3x+9 =0 x = –( –3 ) ± ( –3 ) 2 –4( 1 ) ( 9 ) 2( 1 ) x = 3 ± 9–36 2 x = 3 ± –27 2 x = 3 ± ( –1 ) ( 3 3 ) 2 x = 3 ± 3 3 –1 2 x = 3 ± 3 3 i 2 x 5 = 3–3 3 i 2 x 6 = 3+3 3 i 2
9. Hallar las raíces cúbicas de 8.
   x 3 =8 x 3 –8 =0 ( x–2 ) ( x 2 +2x+4 ) =0 x 1 –2 =0 x 1 =2 x 2 +2x+4 =0 x = –2 ± 2 2 –4( 1 ) ( 4 ) 2( 1 ) x = –2 ± 4–16 2 x = –2 ± –12 2 x = –2 ± ( –1 ) ( 3 ) ( 2 2 ) 2 x = –2 ± 2 –1 3 2 x = 2 ( –1 ± 3 i ) 2 x 2 =–1+ 3 i x 3 =–1– 3 i
10. Hallar las raíces cuartas de 64.
    x 4 =64 x 4 –64 =0 ( x 2 +8 ) ( x 2 –8 ) =0 x 2 –8 =0 x 2 =8 x = ± 8 x = ± 2 3 x = ± 2 2 x 1 =2 2 x 2 =–2 2 x 2 +8 =0 x 2 =–8 x = ± –8 x = ± – 2 3 x = ± 2 2 –1 x 1 =2 2 i x 2 =–2 2 i