Question

If (x + a)(x + b)(x + c) = x³ + 14x² + 59x + 70, find the value of `"a"/"bc" + "b"/"ac" + "c"/"ab"`

Answer 1

(x + a)(x + b)(x + c) = x³ + 14x² + 59x + 70

x³ + (a + b + c)x² + (ab + bc + ac)x + abc = x³ + 14x² + 59x + 70

a + b + c = 14, ab + bc + ac = 59, abc = 70

`"a"/"bc" + "b"/"ac" + "c"/"ab" = ("a"^2 + "b"^2 + "c"^2)/"abc"`

= `(("a" + "b" + "c")^2 - 2("ab" + "bc" + "ac"))/"abc"`

= `(14^2 - 2(59))/70`

= `(196 - 118)/70`

= `78/70`

= `39/35`