Question

if a + b + c is equal to 6 a square + b square + c square is equal to 12 find the value of a cube plus b cube plus c cube - 3abc​

Answer 1

Answer:

a+b+c=6,a

2

+b

2

+c

2

=14,a

3

+b

3

+c

3

=36

(a+b+c)=a

2

+b

2

+c

2

+2(ab+bc+ca)

⟹2(ab+bc+ca)=(6)

2

−14

⟹2(ab+bc+ca)=(6)

2

−14

=36−14=22

ab+bc+ca=11

Now ,we know a

3

+b

3

+c

3

−3abc=(a+b+c)(a

2

+b

2

+c

2

−(ab+bc+ca))

⟹36−3abc=6(14−11)

⟹36−3abc=6×3=18

⟹3abc=18

⟹abc=6

Answer 2

Answer:

a +b+c= 6 (1)

a²+b²+c²= 12 (2)

from this we get values of a b c

a=2

b=2

c=2

hence,

a³+b³+c³-3abc = 2³+2³+2³-3(2) (2) (2)

= 8+8+8-24

= 24-24

= 0

hence zero 0️⃣ is the final answer