Der Ausdruck 10x ^ 2-x-24 kann als (Ax-8) (Bx + 3) geschrieben werden, wobei A und B ganze Zahlen sind. Was ist AB + B?

Antworten:

# AB + B = 12, 65/8 #

# 10x ^ 2-x-24 = (Axe-8) (Bx + 3) #

# 10x ^ 2-x-24 = ABx ^ 2 + 3Ax-8Bx-24 #

# 10x ^ 2-x-24 = ABx ^ 2- (8B-3A) x-24 #

# AB = 10 #

# 8B-3A = 1,:. 8B = 1 + 3A, B = (1 + 3A) / 8 #

# (A (1 + 3A)) / 8 = 10 #

# 3A ^ 2 + A-80 = 0 #

#A = (-1 + -sqrt (1-4 (3) (-80))) / 6 = (-1 + -sqrt961) / 6 = (-1 + -31) / 6 #

# A = 5, -16 / 3 #

# A = 5,:. B = 2,:. AB + B = 10 + 2 = 12 #

# A = -16 / 3,:. B = -15 / 8,. AB + B = 10-15 / 8 = 65/8 #