a+b+c=6
a²+b²+c²=14
a³+b³+c³=36
abc=
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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
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