SSC CPO 2019 PYQ — Question 140

Understanding

Application

a + b + c = 6 and

a² + b² + c² = 38

Use formula:

(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx

So,

6² = 38 + 2ab + 2bc + 2ca

⇒ (ab + bc + ca) = (36 – 38)/2

⇒ (ab + bc + ca) = -1

Now,

a(b² + c²) + b(c² + a²) + c(a² + b²) + 3abc

⇒ a (38 – a²) + b(38 – b²) + c(38 – c²) + 3abc

⇒ 38a + 38b + 38c – (a³ + b³ + c³) + 3abc

⇒ 38(a + b + c) – {(a³ + b³ + c³) – 3abc}

Now use the formula:

x³ + y³ +z³ – 3xyz = (x + y + z) (x² + y² + z² – (xy + yz + zx))

38(a + b + c) – {(a³ + b³ + c³) – 3abc}

⇒ (38 × 6) – {(a + b + c) (a² + b² + c² – ab – bc – ca)}

⇒ (38 × 6) – {6 × (38 – (– 1))}

⇒ (38 × 6) – (6 × 38) – (6 × 1)

⇒ -6