Question

find the value of a cube plus b cube plus c cube - 3abc then a + b + C is equal to 8 and a b + BC + CA is equal to 25

Answer 1

Given :

• a + b + c = 8

• ab + bc + ca = 25

To Find :

• Value of a³ + b³ + c³ - 3abc

Solution :

We know that

★ a³ + b³ + c³ - 3abc = (a+b+c) (a² + b² + c² - ab - bc - ca)

→ a³ + b³ + c³ - 3abc = (a+b+c) {(a² + b² + c²) - (ab + bc + ca)}....i)

Clearly,we require the values of a + b + c, a² + b² + c² and ab + bc + ca to obtain the values of a³ + b³ + c³ - 3abc. We're given the values of a + b + c and ab + bc + ca. So,let us first obtain value of a² + b² + c².

We know that,

★ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

→ (a + b + c)² = (a² + b² + c²) + 2(ab + bc + ca)

Put the values of a + b + c and ab + bc + ca

→ (8)² = a² + b² + c² + 2(25)

→ 64 = a² + b² + c² + 50

→ a² + b² + c² = 64 - 50

→ a² + b² + c² = 14

Now,putting a + b + c = 8 and ab + bc + ca = 25 and a² + b² + c² = 14 in equation i), we get :

★ a³ + b³ + c³ - 3abc = (a+b+c) {(a² + b² + c²) - (ab + bc + ca)}

→ a³ + b³ + c³ - 3abc = (8) (14 - 25)

→ a³ + b³ + c³ - 3abc = 8 × -11

→ a³ + b³ + c³ - 3abc = - 88

$\therefore$ Value of a³ + b³ + c³ - 3abc = -88

Answer 2

Step-by-step explanation:

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