If a + b + c = 3, ab + bc + ca = -10 and abc = -24. then the value of a²overbc + b²overac + c²overab is:

If a + b + c = 3, ab + bc + ca = -10 and abc = -24. then…

If a + b + c = 3, ab + bc + ca = -10 and abc = -24. then the value of $a^2\over{bc}$ + $b^2\over{ac}$ + $c^2\over{ab}$ is:

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. $-15\over8$ .

a³ + b³ + c³ = (a + b + c)³ - 3(a + b + c)(ab + bc + ca) + 3abc

⇒ a³ + b³ + c³ = (3)³ - 3 × 3 × (-10) + 3(-24)

⇒ a³ + b³ + c³ = 27 + 90 - 72 = 45

⇒ $a^2\over{bc}$ + $b^2\over{ac}$ + $c^2\over{ab}$

⇒ $a^3+b^3+c^3\over abc$ = $45\over -24$ = $-15\over8$