1.

If a+b+c=9 and ab+bc+ca=26 then find the value of

Answer»

ANSWER:

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 + b ² + 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.


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