a + b + c = 25 and AB + BC + CA equals to 10 then prove that a cube plus b cube plus c cube minus 3 ABC = 2 - 25
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We know that
(a+b+c)2=a2+b2+c2+2(ab+bc+ca)
a2+b2+c2=625-20=605
Now
a3+b3+c3 -3abc= (a+b+c)(a2+b2+c2-(ab+bc+ca)
a3 +b3+c3-3abc= 25(605-10)
. =25*595
(a+b+c)2=a2+b2+c2+2(ab+bc+ca)
a2+b2+c2=625-20=605
Now
a3+b3+c3 -3abc= (a+b+c)(a2+b2+c2-(ab+bc+ca)
a3 +b3+c3-3abc= 25(605-10)
. =25*595
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