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Barg3 Barg3
  • 30-08-2016
  • Mathematics
Answered

if 2x= a+b+c

show that


(x-a)² + (x-b)² + (x-c)² + x² = a² + b² + c²

Verified Answer :

parry1
parry1 parry1
  • 30-08-2016

here is solution all the 2 are cancelled. please ask about any doubt or something

View image parry1
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caylus
caylus caylus
  • 30-08-2016

Hello,

\(\boxed{(x-a)^2+(x-b)^2+(x-c)^2+x^2}\ \\ =(x^2-2ax+a^2)+(x^2-2bx+b^2)+(x^2-2cx+c^2)+\ x^2\\ =3x^2-2x(a+b+c)+x^2+a^2+b^2+c^2\\ =3x^2-4x^2+x^2+a^2+b^2+c^2\\ =\boxed{a^2+b^2+c^2}\)

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