If a + b + c =5 and ab + bc +ca = 10 , Prove that a³ + b³ + c³ - 3abc = -25
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Hey!!!...here is ur answer
As we know that..
a^3+b^3+c^3 - 3 a b c = (a+b+c)(a^2+b^2+c^2 - a b - b c - a c)
And also know that
(a + b + c)^2 = a^2+ b^2+ c^2+ 2ab + 2bc + 2ca
(5)^2= a^2+ b^2+ c^2+2 (10)
a^2+ b^2+ c^2=5
Now...
a^3+b^3+c^3 - 3 a b c = (a+b+c)(a^2+b^2+c^2 - a b - b c - a c)
a^3+b^3+c^3 - 3 a b c =(5)[5-(10)]
a^3+b^3+c^3 - 3 a b c =5×(-5)
a^3+b^3+c^3 - 3 a b c =-25 HENCE PROVED
Hope it will help you
As we know that..
a^3+b^3+c^3 - 3 a b c = (a+b+c)(a^2+b^2+c^2 - a b - b c - a c)
And also know that
(a + b + c)^2 = a^2+ b^2+ c^2+ 2ab + 2bc + 2ca
(5)^2= a^2+ b^2+ c^2+2 (10)
a^2+ b^2+ c^2=5
Now...
a^3+b^3+c^3 - 3 a b c = (a+b+c)(a^2+b^2+c^2 - a b - b c - a c)
a^3+b^3+c^3 - 3 a b c =(5)[5-(10)]
a^3+b^3+c^3 - 3 a b c =5×(-5)
a^3+b^3+c^3 - 3 a b c =-25 HENCE PROVED
Hope it will help you
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