Question

if a+b+c=12
${a}^{2} + {b}^{2} + {c}^{2}$


=90 find
${a}^{3} + {b}^{3} + {c}^{3}$
-3abc

Answer 1

Hi ,

It is given that ,

a+ b + c = 12 ---( 1 )

a² + b² + c² = 90 ------( 2 )

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

= ( 12 )² - 90

= 144 - 90

= 54

therefore ,

ab + bc + ca = 54/2

ab + bc + ca = 27 -----( 3 )

****************

we know the algebraic identity ,

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

= 12 [ 90 - 27 ]

= 12 × 63

= 756

I hope this helps you.

: )