Ipagpalagay na g (x) = 5x ^ 4-15x ^ 2-32. Paano mo malutas ang equation para sa x kung g (x) = - 32? Paano ang tungkol sa g (x) = 58?

Sagot:

Kaso 1: #g (x) = - 32 kulay rarr (green) (x in {0, + - sqrt (93)}) #

Kaso 2: #g (x) = 58 rarr color (green) (x sa {+ -sqrt (6), + - sqrt (3) i}) #

Paliwanag:

Ibinigay: #color (asul) (g (x) = 5x ^ 4-15x ^ 2-32 #

Bahagi 1: #color (pula) ("Kung" g (x) = - 32) #

#color (pula) (- 32) = kulay (asul) (5x ^ 4-15x ^ 2-32) #

#rarr kulay (asul) (5x ^ 4-15x ^ 2) = 0 #

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

#rarr {{x ^ 2 = 0, color (white) ("X") orcolor (white) ("X"), x ^ 2-3 = 0), (rarrx = 0,, rarrx = + - sqrt (3)):} #

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

Bahagi 2: #color (pula) ("Kung" g (x) = 58) #

#color (pula) (58) = kulay (asul) (5x ^ 4-15x ^ 2-32) #

#rarr kulay (asul) ("5x ^ 4-15x ^ 2) -90 = 0 #

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

#rarr {(x ^ 2-6) = 0, kulay (puti) ("X") orcolor (puti) ("X"), x ^ 2 + 3 = 0), (rarrx = + - sqrt (6),, rarrx = + - sqrt (3) i):} #

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