Question

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 a b c

Answer 1

(a+b+c)=12
a^2+b^2+c^2=90
A^3+b^3+c^3-abc

I think if we can use a=9 b=3 and =0
as 9+3+0=12&81+9+0=90
so 9^3+3^3+0^3-3★9★0=756

Answer 2

Answer:

Value of a³ + b³ + c³ - 3abc is 756.

Step-by-step explanation:

We are given,   a + b + c = 12    and  a² + b² + c² = 90

To find: a³ + b³ + c³ - 3abc

First we use following identity to find value of ab + cb + ac,

( 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.