A 2 b 2 c 2 ab bc ca
Asked by admin @ in Math viewed by 349 People
a2+b2+c2-ab-bc-ca Whatever the value of a, b, c be the equation can never be negative. Prove it.. I got this Riddle from my Maths Teacher. Help me prove this.
Answered by admin @
A^2+b^2+c^2-ab-bc-ac
=1/2(2a^2+2b^2+2c^2-2ab-2bc-2ac)
=1 /2{(a-b)^2+(b-c)^2+(c-a)^2}
if a,b,c are real numbers then,(a-b)^2,(b-c)^2and(c-a)^2 are positive square of every real number is positive. So,
a^2+b^2+c^2-ab-bc-ca is always positive
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