Denimo, da je g (x) = 5x ^ 4-15x ^ 2-32. Kako rešiti enačbo za x, če je g (x) = - 32? Kaj pa g (x) = 58?

Odgovor:

Primer 1: #g (x) = - 32 rarr barve (zelena) (x v {0, + - sqrt (93)}) #

Primer 2: #g (x) = 58 rarr barva (zelena) (x v {+ -sqrt (6), + - sqrt (3) i}) #

Pojasnilo:

Glede na: #barva (modra) (g (x) = 5x ^ 4-15x ^ 2-32 #

1. del: #barva (rdeča) ("Če" g (x) = - 32) #

#barva (rdeča) (- 32) = barva (modra) (5x ^ 4-15x ^ 2-32) #

#rarr barva (modra) (5x ^ 4-15x ^ 2) = 0 #

#rarr 5xxx ^ 2xx (x ^ 2-3) = 0 #

#rarr {(x ^ 2 = 0, barva (bela) ("X") ali barva (bela) ("X"), x ^ 2-3 = 0), (rarrx = 0,, rarrx = + - sqrt (3)):} #

#x v {-sqrt (3), 0, + sqrt (3)} #

2. del: #barva (rdeča) ("Če" g (x) = 58) #

#barva (rdeča) (58) = barva (modra) (5x ^ 4-15x ^ 2-32) #

#rarr barva (modra) ("5x ^ 4-15x ^ 2) -90 = 0 #

#rarr 5xx (x ^ 2-6) xx (x ^ 2 + 3) = 0 #

#rarr {((x ^ 2-6) = 0, barva (bela) ("X") ali barva (bela) ("X"), x ^ 2 + 3 = 0), (rarrx = + - sqrt (6)), rarrx = + - sqrt (3) i):} #

#x v {-sqrt (6), + sqrt (6), - sqrt (3) i, + sqrt (3) i} #