a , b , c are three real numbers such that a + b + c = 7 , a 2 + b 2 + c 2 = 35 and a 3 + b 3 + c 3 = 151 . Find the value of abc.
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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.
(a+b+c)^2=
a^2+b^2+c^2+2ab+2bc+2ca
49=35+2ab+2bc+2ac
ab+bc +ca =7
a^3+b^3+c^3-3abc=
(a+b+c)(a^2+b^2+c^2-ab-bc-ca)
151-3abc=7(35-7)
151-3abc=196
3abc=-45
abc=-15
(a+b+c)^2=
a^2+b^2+c^2+2ab+2bc+2ca
49=35+2ab+2bc+2ac
ab+bc +ca =7
a^3+b^3+c^3-3abc=
(a+b+c)(a^2+b^2+c^2-ab-bc-ca)
151-3abc=7(35-7)
151-3abc=196
3abc=-45
abc=-15
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