if a + b + c = 9 and a^2 + b^2 + c^2= 35 find the value of a^3 + b^3+c^3-3abc
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a+b+c =9
by squaring on both sides
(a+b+c)^2 = 9^2
a^2 + b^2 + c^2 + 2 ab + 2b c + 2 a = 81
35 + ( 2ab+2bc+2ca)=81
2ab + 2bc + 2ca = 81 -35
2 ab + 2bc + 2ca = 46
2 ( ab+ bc+ ca) = 46
ab+ bc+ ca = 23
now ,
( a +b+ c )(a^2+ b^2+ c^2 - ab -bc -ca)
= 9 (35-23)
9 (12)
=108
hope it helps....
by squaring on both sides
(a+b+c)^2 = 9^2
a^2 + b^2 + c^2 + 2 ab + 2b c + 2 a = 81
35 + ( 2ab+2bc+2ca)=81
2ab + 2bc + 2ca = 81 -35
2 ab + 2bc + 2ca = 46
2 ( ab+ bc+ ca) = 46
ab+ bc+ ca = 23
now ,
( a +b+ c )(a^2+ b^2+ c^2 - ab -bc -ca)
= 9 (35-23)
9 (12)
=108
hope it helps....
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