a, b, c are three real numbers such that a + b + c = 7, a2 + b2 + c2 = 35 and a3 + b3 + c3 = 151. Find the value of abc.
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(a+b+c)^3=a^3+b^3+c^3+3×a(b^2+c^2)+3b(a^2+c^2)+3c(a^2+b^2)+6abc
7^3=151+3a(35-a^2)+3b(35-b^2)+3c(35-c^2)+6abc
343=151-3(a3+b3+c3)+105(a+b+c)+6abc
6abc=343-735+302=-90
abc= -15
7^3=151+3a(35-a^2)+3b(35-b^2)+3c(35-c^2)+6abc
343=151-3(a3+b3+c3)+105(a+b+c)+6abc
6abc=343-735+302=-90
abc= -15
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