if 1/a2+1/b2+1/c2=1/ab+1/bc+1/ca then find the value of a+b+c/2a
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Step-by-step explanation:
1/a^2 + 1/b^2 + 1/c^2 = 1/ab + 1/bc + 1/ ac
=> 2/a^2 + 2/b^2 + 2/c^2 = 2/ab + 2/ bc + 2/ac
=>1/a^2 - 2/ab + 1/b^2 + 1/b^2 - 2/bc + 1/c^2 + 1/c^2 - 2/ac + 1/a^2 = 0
=> (1/a - 1/b)^2 + (1/b - 1/c)^2 + (1/c - 1/a)^2 = 0
=> 1/a - 1/b = 0, 1/b - 1/c = 0, 1/c - 1/a = 0 ( since sum of the perfect squares is 0)
=> 1/a = 1/b, 1/b = 1/c , 1/c = 1/a
=> a = b,. b = c, c = a => a= b = c
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