Question

Hii anyone can solve it​

Answer 1

Answer:

756

Step-by-step explanation:

a+b+c = 9

a²+b²+c² = 83

(a+b+c)² - 2(ab+bc+ca) = 83

81 - 2(ab+bc+ca) = 83

-2(ab+bc+ca) = 2

ab+bc+ca = -1

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a³+b³+c³ - 3abc

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

= (a + b + c) [ (a²+b²+c²) - (ab+bc+ca)]

= 9 * [83 - (-1)]

= 9 * 84

=  756

Answer 2

Question :

If a + b + c = 9 and a² + b² + c² = 83, find the value of a³ + b³ + c³ - 3abc.

Solution :

→ (a + b + c)² - 2(ab + bc + ca) = 83

→ (9)² - 2(ab + bc + ca) = 83

[As a + b + c = 9 (given)]

→ 81 - 2(ab + bc + ca) = 83

→ - 2(ab + bc + ca) = 83 - 81

→ - 2(ab + bc + ca) = 2

→ ab + bc + ca = - 1

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Now...

→ a³ + b³ + c³ - 3abc = a³ + b³ + c³ - 3abc

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

→ (a + b + c) [a ² + b² + c² - (ab + bc + ca)]

→ (9) [83 - (-1)]

→ 9 (83 + 1)

→ 9 (84)

→ 756

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a³ + b³ + c³ - 3abc = 756

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