Question

if a is equal to a + b + C is equal to 12 a square + b square + c square is equal to 90 find the value of a cube plus b cube plus c cube minus 3 ABC

Answer 1

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Answer 2

Answer:

Value of a³ + b³ + c³ - 3abc is 756.

Step-by-step explanation:

Given:

a + b + c = 12

a² + b² + c² = 90

To find: a³ + b³ + c³ - 3abc

We use the identity,

( a + b + c )² = a² + b² + c² + 2ab + 2cb + 2ac

( 12 )² = 90 + 2ab + 2cb + 2ac

2 (ab + cb + ac) = 144-90

ab + cb + ac = 54/2

ab + cb + ac = 27

Now using identity,

a³ + b³ + c³ - 3abc = ( a + b + c)( a² + b² + c² - ab - cb - ac )

                              = ( 12 ) ( 90 - (ab + cb + ac))

                              = ( 12 ) ( 90 - (27))

                              = ( 12 ) ( 63 )

                              = 756

Therefore, Value of a³ + b³ + c³ - 3abc is 756.