El profesor se sorprenderá mucho al ver tu solución correcta😉
x*x*x*x - 16*x*x + 20*x - 25 = 0
_________________________________________________________________________________________________________________________________________________ / _____________________ / / _____ / 64 / 1637 10*\/ 331 40 22 / -- - 2*3 / - ---- + ---------- + ---------------------------------------------------------------------------- + ---------------------------- / 3 \/ 27 3 __________________________________________________________________ _____________________ __________________________________________________________________ / / _____________________ / _____ / _____________________ / / / _____ / 1637 10*\/ 331 / / _____ / / 32 / 1637 10*\/ 331 22 9*3 / - ---- + ---------- / 32 / 1637 10*\/ 331 22 / / -- + 2*3 / - ---- + ---------- - ---------------------------- \/ 27 3 / -- + 2*3 / - ---- + ---------- - ---------------------------- / / 3 \/ 27 3 _____________________ / 3 \/ 27 3 _____________________ / / / _____ / / _____ / / / 1637 10*\/ 331 / / 1637 10*\/ 331 / / 9*3 / - ---- + ---------- / 9*3 / - ---- + ---------- \/ \/ \/ 27 3 \/ \/ 27 3 x1 = ---------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------- 2 2
_____________________________________________________________________________________________________________________________________________________ / _____________________ / / _____ / 64 / 1637 10*\/ 331 40 22 I* / - -- + 2*3 / - ---- + ---------- + ------------------------------------------------------------------------------ - ---------------------------- ____________________________________________________________________ / 3 \/ 27 3 ____________________________________________________________________ _____________________ / | _____________________ | / / | _____________________ | / _____ / | / _____ | / / | / _____ | / 1637 10*\/ 331 / |32 / 1637 10*\/ 331 22 | / / |32 / 1637 10*\/ 331 22 | 9*3 / - ---- + ---------- / |-- + 2*3 / - ---- + ---------- - ----------------------------| / / |-- + 2*3 / - ---- + ---------- - ----------------------------| \/ 27 3 / |3 \/ 27 3 _____________________| / / |3 \/ 27 3 _____________________| / | / _____ | / / | / _____ | / | / 1637 10*\/ 331 | / / | / 1637 10*\/ 331 | / | 9*3 / - ---- + ---------- | / / | 9*3 / - ---- + ---------- | \/ | \/ 27 3 | \/ \/ | \/ 27 3 | x2 = ------------------------------------------------------------------------------ - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- 2 2
_____________________________________________________________________________________________________________________________________________________ / _____________________ / / _____ / 64 / 1637 10*\/ 331 40 22 I* / - -- + 2*3 / - ---- + ---------- + ------------------------------------------------------------------------------ - ---------------------------- ____________________________________________________________________ / 3 \/ 27 3 ____________________________________________________________________ _____________________ / | _____________________ | / / | _____________________ | / _____ / | / _____ | / / | / _____ | / 1637 10*\/ 331 / |32 / 1637 10*\/ 331 22 | / / |32 / 1637 10*\/ 331 22 | 9*3 / - ---- + ---------- / |-- + 2*3 / - ---- + ---------- - ----------------------------| / / |-- + 2*3 / - ---- + ---------- - ----------------------------| \/ 27 3 / |3 \/ 27 3 _____________________| / / |3 \/ 27 3 _____________________| / | / _____ | / / | / _____ | / | / 1637 10*\/ 331 | / / | / 1637 10*\/ 331 | / | 9*3 / - ---- + ---------- | / / | 9*3 / - ---- + ---------- | \/ | \/ 27 3 | \/ \/ | \/ 27 3 | x3 = ------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- 2 2
_________________________________________________________________________________________________________________________________________________ / _____________________ / / _____ / 64 / 1637 10*\/ 331 40 22 / -- - 2*3 / - ---- + ---------- + ---------------------------------------------------------------------------- + ---------------------------- __________________________________________________________________ / 3 \/ 27 3 __________________________________________________________________ _____________________ / _____________________ / / _____________________ / _____ / / _____ / / / _____ / 1637 10*\/ 331 / 32 / 1637 10*\/ 331 22 / / 32 / 1637 10*\/ 331 22 9*3 / - ---- + ---------- / -- + 2*3 / - ---- + ---------- - ---------------------------- / / -- + 2*3 / - ---- + ---------- - ---------------------------- \/ 27 3 / 3 \/ 27 3 _____________________ / / 3 \/ 27 3 _____________________ / / _____ / / / _____ / / 1637 10*\/ 331 / / / 1637 10*\/ 331 / 9*3 / - ---- + ---------- / / 9*3 / - ---- + ---------- \/ \/ 27 3 \/ \/ \/ 27 3 x4 = - ---------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------- 2 2
x4 = -sqrt(-2*(-1637/27 + 10*sqrt(331)/3)^(1/3) + 22/(9*(-1637/27 + 10*sqrt(331)/3)^(1/3)) + 64/3 + 40/sqrt(-22/(9*(-1637/27 + 10*sqrt(331)/3)^(1/3)) + 2*(-1637/27 + 10*sqrt(331)/3)^(1/3) + 32/3))/2 - sqrt(-22/(9*(-1637/27 + 10*sqrt(331)/3)^(1/3)) + 2*(-1637/27 + 10*sqrt(331)/3)^(1/3) + 32/3)/2
suma
_________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ / _____________________ / _____________________ / _____________________ / _____________________ / / _____ / / _____ / / _____ / / _____ / 64 / 1637 10*\/ 331 40 22 / 64 / 1637 10*\/ 331 40 22 / 64 / 1637 10*\/ 331 40 22 / 64 / 1637 10*\/ 331 40 22 / -- - 2*3 / - ---- + ---------- + ---------------------------------------------------------------------------- + ---------------------------- I* / - -- + 2*3 / - ---- + ---------- + ------------------------------------------------------------------------------ - ---------------------------- I* / - -- + 2*3 / - ---- + ---------- + ------------------------------------------------------------------------------ - ---------------------------- / -- - 2*3 / - ---- + ---------- + ---------------------------------------------------------------------------- + ---------------------------- / 3 \/ 27 3 __________________________________________________________________ _____________________ __________________________________________________________________ ____________________________________________________________________ / 3 \/ 27 3 ____________________________________________________________________ _____________________ ____________________________________________________________________ / 3 \/ 27 3 ____________________________________________________________________ _____________________ __________________________________________________________________ / 3 \/ 27 3 __________________________________________________________________ _____________________ / / _____________________ / _____ / _____________________ / | _____________________ | / / | _____________________ | / _____ / | _____________________ | / / | _____________________ | / _____ / _____________________ / / _____________________ / _____ / / / _____ / 1637 10*\/ 331 / / _____ / | / _____ | / / | / _____ | / 1637 10*\/ 331 / | / _____ | / / | / _____ | / 1637 10*\/ 331 / / _____ / / / _____ / 1637 10*\/ 331 / / 32 / 1637 10*\/ 331 22 9*3 / - ---- + ---------- / 32 / 1637 10*\/ 331 22 / |32 / 1637 10*\/ 331 22 | / / |32 / 1637 10*\/ 331 22 | 9*3 / - ---- + ---------- / |32 / 1637 10*\/ 331 22 | / / |32 / 1637 10*\/ 331 22 | 9*3 / - ---- + ---------- / 32 / 1637 10*\/ 331 22 / / 32 / 1637 10*\/ 331 22 9*3 / - ---- + ---------- / / -- + 2*3 / - ---- + ---------- - ---------------------------- \/ 27 3 / -- + 2*3 / - ---- + ---------- - ---------------------------- / |-- + 2*3 / - ---- + ---------- - ----------------------------| / / |-- + 2*3 / - ---- + ---------- - ----------------------------| \/ 27 3 / |-- + 2*3 / - ---- + ---------- - ----------------------------| / / |-- + 2*3 / - ---- + ---------- - ----------------------------| \/ 27 3 / -- + 2*3 / - ---- + ---------- - ---------------------------- / / -- + 2*3 / - ---- + ---------- - ---------------------------- \/ 27 3 / / 3 \/ 27 3 _____________________ / 3 \/ 27 3 _____________________ / |3 \/ 27 3 _____________________| / / |3 \/ 27 3 _____________________| / |3 \/ 27 3 _____________________| / / |3 \/ 27 3 _____________________| / 3 \/ 27 3 _____________________ / / 3 \/ 27 3 _____________________ / / / _____ / / _____ / | / _____ | / / | / _____ | / | / _____ | / / | / _____ | / / _____ / / / _____ / / / 1637 10*\/ 331 / / 1637 10*\/ 331 / | / 1637 10*\/ 331 | / / | / 1637 10*\/ 331 | / | / 1637 10*\/ 331 | / / | / 1637 10*\/ 331 | / / 1637 10*\/ 331 / / / 1637 10*\/ 331 / / 9*3 / - ---- + ---------- / 9*3 / - ---- + ---------- / | 9*3 / - ---- + ---------- | / / | 9*3 / - ---- + ---------- | / | 9*3 / - ---- + ---------- | / / | 9*3 / - ---- + ---------- | / 9*3 / - ---- + ---------- / / 9*3 / - ---- + ---------- \/ \/ \/ 27 3 \/ \/ 27 3 \/ | \/ 27 3 | \/ \/ | \/ 27 3 | \/ | \/ 27 3 | \/ \/ | \/ 27 3 | \/ \/ 27 3 \/ \/ \/ 27 3 ---------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------- + ------------------------------------------------------------------------------ - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- + - ---------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------- 2 2 2 2 2 2 2 2
=
____________________________________________________________________ __________________________________________________________________ / | _____________________ | / _____________________ / | / _____ | / / _____ / |32 / 1637 10*\/ 331 22 | / 32 / 1637 10*\/ 331 22 / |-- + 2*3 / - ---- + ---------- - ----------------------------| - / -- + 2*3 / - ---- + ---------- - ---------------------------- / |3 \/ 27 3 _____________________| / 3 \/ 27 3 _____________________ / | / _____ | / / _____ / | / 1637 10*\/ 331 | / / 1637 10*\/ 331 / | 9*3 / - ---- + ---------- | / 9*3 / - ---- + ---------- \/ | \/ 27 3 | \/ \/ 27 3
producto
/ _________________________________________________________________________________________________________________________________________________ \ / _____________________________________________________________________________________________________________________________________________________\ / _____________________________________________________________________________________________________________________________________________________\ / _________________________________________________________________________________________________________________________________________________\ | / _____________________ | | / _____________________ | | / _____________________ | | / _____________________ | | / / _____ | | / / _____ | | / / _____ | | / / _____ | | / 64 / 1637 10*\/ 331 40 22 | | / 64 / 1637 10*\/ 331 40 22 | | / 64 / 1637 10*\/ 331 40 22 | | / 64 / 1637 10*\/ 331 40 22 | | / -- - 2*3 / - ---- + ---------- + ---------------------------------------------------------------------------- + ---------------------------- | | I* / - -- + 2*3 / - ---- + ---------- + ------------------------------------------------------------------------------ - ---------------------------- | | I* / - -- + 2*3 / - ---- + ---------- + ------------------------------------------------------------------------------ - ---------------------------- | | / -- - 2*3 / - ---- + ---------- + ---------------------------------------------------------------------------- + ---------------------------- | | / 3 \/ 27 3 __________________________________________________________________ _____________________ __________________________________________________________________| | ____________________________________________________________________ / 3 \/ 27 3 ____________________________________________________________________ _____________________ | | ____________________________________________________________________ / 3 \/ 27 3 ____________________________________________________________________ _____________________ | | __________________________________________________________________ / 3 \/ 27 3 __________________________________________________________________ _____________________ | | / / _____________________ / _____ / _____________________ | | / | _____________________ | / / | _____________________ | / _____ | | / | _____________________ | / / | _____________________ | / _____ | | / _____________________ / / _____________________ / _____ | | / / / _____ / 1637 10*\/ 331 / / _____ | | / | / _____ | / / | / _____ | / 1637 10*\/ 331 | | / | / _____ | / / | / _____ | / 1637 10*\/ 331 | | / / _____ / / / _____ / 1637 10*\/ 331 | | / / 32 / 1637 10*\/ 331 22 9*3 / - ---- + ---------- / 32 / 1637 10*\/ 331 22 | | / |32 / 1637 10*\/ 331 22 | / / |32 / 1637 10*\/ 331 22 | 9*3 / - ---- + ---------- | | / |32 / 1637 10*\/ 331 22 | / / |32 / 1637 10*\/ 331 22 | 9*3 / - ---- + ---------- | | / 32 / 1637 10*\/ 331 22 / / 32 / 1637 10*\/ 331 22 9*3 / - ---- + ---------- | | / / -- + 2*3 / - ---- + ---------- - ---------------------------- \/ 27 3 / -- + 2*3 / - ---- + ---------- - ---------------------------- | | / |-- + 2*3 / - ---- + ---------- - ----------------------------| / / |-- + 2*3 / - ---- + ---------- - ----------------------------| \/ 27 3 | | / |-- + 2*3 / - ---- + ---------- - ----------------------------| / / |-- + 2*3 / - ---- + ---------- - ----------------------------| \/ 27 3 | | / -- + 2*3 / - ---- + ---------- - ---------------------------- / / -- + 2*3 / - ---- + ---------- - ---------------------------- \/ 27 3 | | / / 3 \/ 27 3 _____________________ / 3 \/ 27 3 _____________________ | | / |3 \/ 27 3 _____________________| / / |3 \/ 27 3 _____________________| | | / |3 \/ 27 3 _____________________| / / |3 \/ 27 3 _____________________| | | / 3 \/ 27 3 _____________________ / / 3 \/ 27 3 _____________________ | | / / / _____ / / _____ | | / | / _____ | / / | / _____ | | | / | / _____ | / / | / _____ | | | / / _____ / / / _____ | | / / / 1637 10*\/ 331 / / 1637 10*\/ 331 | | / | / 1637 10*\/ 331 | / / | / 1637 10*\/ 331 | | | / | / 1637 10*\/ 331 | / / | / 1637 10*\/ 331 | | | / / 1637 10*\/ 331 / / / 1637 10*\/ 331 | | / / 9*3 / - ---- + ---------- / 9*3 / - ---- + ---------- | | / | 9*3 / - ---- + ---------- | / / | 9*3 / - ---- + ---------- | | | / | 9*3 / - ---- + ---------- | / / | 9*3 / - ---- + ---------- | | | / 9*3 / - ---- + ---------- / / 9*3 / - ---- + ---------- | |\/ \/ \/ 27 3 \/ \/ 27 3 | |\/ | \/ 27 3 | \/ \/ | \/ 27 3 | | |\/ | \/ 27 3 | \/ \/ | \/ 27 3 | | | \/ \/ 27 3 \/ \/ \/ 27 3 | |---------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------|*|------------------------------------------------------------------------------ - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|------------------------------------------------------------------------------ + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|- ---------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------| \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 /
=
-25
-25
x1 = -4.63457658462957
x2 = 0.561441654160788 - 1.10492607167109*i
x3 = 3.51169327630799
x4 = 0.561441654160788 + 1.10492607167109*i
x4 = 0.561441654160788 + 1.10492607167109*i