Question

find the vale of a³+b³+c³‐3abc,when a+b+c=14​

Answer 1

Answer:a³ + b³ + c³- 3abc = 45

Step-by-step explanation:Given,

a + b + c = 15

ab + bc + ca = 74

We need to find the value of a³ + b³ + c³- 3abc

We know,

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

Now we need to find the value of  a² + b² + c²

We also know,

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

Putting the value of a + b + c = 15 and ab + bc + ca = 74

( 15 )² = a² + b² + c² + 2 ( 74 )

225 = a² + b² + c² + 148

a² + b² + c² = 225 - 148

a² + b² + c² = 77

Now,

Substituting value in the formula for a³ + b³ + c³- 3abc

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

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

a³ + b³ + c³- 3abc = ( 15 ) ( 77 - ( 74 ) )

a³ + b³ + c³- 3abc =  ( 15 ) ( 3 )

a³ + b³ + c³- 3abc = 45

Hence,

a³ + b³ + c³- 3abc = 45

Hopes it helps

Answer 2

Hi friend,

here is your answer

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Answer:

2744

Step-by-step explanation:

if a + b + c = 14

(a + b + c)^3 = 14^3 = 2744

we know the formula (a + b + c)^3 = a^3 + b^3 + c^3 + 3abc

so, a^3 + b^3 + c^3 + 3abc = 2744

hope it helps you and you understood

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