Question

A+b+c=6 and ab+bc+ ca =11 find value of a^3b^3c^3

Answer 1

Step-by-step explanation:

Correct Question :-

a + b + c = 6 and ab + bc + ca = 11. Find the value of a³ + b³ + c³ - 3abc

Solution :-

Given -

• a + b + c = 6
• ab + bc + ca = 11

→ -(-ab - bc - ca) = 11

→ -ab - bc - ca = -11

To Find -

• Value of a³ + b³ + c³ - 3abc

As we know that :-

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

Now,

a + b + c = 6

Squaring both sides :-

→ (a + b + c)² = (6)²

→ a² + b² + c² + 2(ab + bc + ca) = 36

→ a² + b² + c² + 2(11) = 36

→ a² + b² + c² = 36 - 22

→ a² + b² + c² = 14

Now,

→ a³ + b³ + c³ - 3abc = (6)(14 - 11)

→ a³ + b³ + c³ - 3abc = 6 × 3

→ a³ + b³ + c³ - 3abc = 18

Hence,

The value of a³ + b³ + c³ - 3abc is 18.