Question

if a+b+c= 9 and ab+ bc+ ca= 26 then the value of a3+b3+c3-3abc is​

Answer 1

▪︎Given:-

• a + b + c = 9

• ab + bc + ac = 26

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▪︎To Find:-

• a³ + b³ + c³ - 3abc

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▪︎Formula Used:-

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

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

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▪︎Solution:-

➥ By using the Formula

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

➥ Putting given values in Formula ;

➟ (9)² = a² + b² + c² + 2(26)

➥ Solving the equation to get the value of (a² + b² + c²)

➟ 81 = a² + b² + c² + 52

➟ 81 - 52 = a² + b² + c²

➟ a² + b² + c² = 29 ----- eq.1

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➥ Now,

By using the Formula

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

➥ Putting the given values and eq. 1 in Formula

➟ a³ + b³ + c³ - 3abc = 9 × (29 - 26)

➟ a³ + b³ + c³ - 3abc = 9 × 3

➟ a³ + b³ + c³ - 3abc = 27

Hence the value of a³ + b³ + c³ - 3abc is 27.

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▪︎Answer:-

• a³ + b³ + c³ - 3abc = 27.

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