Question

If a+b+c=9 and a^2 + b^2 + c^2 = 35 , find the value of a^3+b^3+c^3 - 3abc .

Answer 1

Answer:

GIVEN:-

If a+b+c = 9 and a²+b²+c²= 35.

TO FIND:-

a³+b³+c³-3abc.

IDENTITIES USED:-

{\boxed{\rm{(a+b+c)^2}}}

(a+b+c)

2

{\boxed{\rm{a^3+b^3+c^3-3abc}}}

a

3

+b

3

+c

3

−3abc

.

Now,

First we have to find the value of ab+bc+ac.

\implies\rm{(a+b+c)^2=a^2+b^2+2(ab+bc+ac)}⟹(a+b+c)

2

=a

2

+b

2

+2(ab+bc+ac)

\implies\rm{(9)^2=35+2(ab+bc+ac)}⟹(9)

2

=35+2(ab+bc+ac)

\implies\rm{81-35=2(ab+bc+ac)}⟹81−35=2(ab+bc+ac)

\implies\rm{46=2(ab+bc+ac)}⟹46=2(ab+bc+ac)

\implies\rm{ab+bc+ac=23}⟹ab+bc+ac=23 .

Answer 2

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Solved in the attachment

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