maths

1)設每款貼紙的原價 $ x ,多付 $10 及售價均降低 $1 購得款數 - 原來購得款數 = 14(54 + 10)/(x - 1) - 54/x = 1464x - 54(x - 1) = 14x(x - 1)10x + 54 = 14(x² - x)5x + 27 = 7x² - 7x7x² - 12x - 27 = 0(7x + 9) (x - 3) = 0x = - 9/7 (捨) 或 x = 3每款貼紙的原價 = $ 3
2)f(x) = x³ - 7x + 6= x³ - x - (6x - 6)= x(x² - 1) - 6(x - 1)= x(x + 1)(x - 1) - 6(x - 1) = (x - 1)(x² - 5x + 6)= (x - 1)(x - 2)(x - 3) is divisible by x^2-3x+k ,So x^2-3x+k = (x - 1)(x - 2) = x² - 3x + 2k = 2
3)3cos² x - 4cosx + 1 = 0(3cos x - 1) (cos x - 1) = 0cos x = 1/3 or 12 roots for cos x = 1/3 for 0° =< x < 360°1 root for cos x = 1 for 0° =< x < 360°The equation have 3 roots.