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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⇒a3+b3+c3-3abc
⇒(a+b+c)(a2+b2+c2-ab-bc-ac)
⇒(a+b+c)^2
⇒a2+b2+c2+2ab+2bc+2ac
⇒(a+b+c)(a2+b2+c2-ab-bc-ac)
⇒(a+b+c)^2
⇒a2+b2+c2+2ab+2bc+2ac
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