Question

If a+b+c=9 and ab+bc+ca=26 then find a3+b3+c3-3abc

Answer 1

Answer :-

→ 27 .

Step-by-step explanation :-

We have,

→ a + b + c = 9 .

And, ab + bc + ca = 26 .

Now, using Identity :-)

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

→ ( 9 )² = a² + b² + c² + 2( 26 ) .

→ 81 = a² + b² + c² + 52 .

→ 81 - 52 = a² + b² + c² .

•°• a² + b² + c² = 29 .

Now, using Identity :-)

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

= ( 9 )[ 29 - ( 26 ) ] .

= ( 9 ) ( 29 - 26 ) .

= 9 × 3 .

•°• a³ + b³ + c³ - 3abc = 27 .

Hence, it is solved.

Answer 2

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