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(b-c)x^2 + (c-a)x +(a-b) =0 are equal to 2b=a+c
x=1 satisfying the equation
since it's roots are equal. So, 1 & 1 are it's roots
product of roots = 1×1 = 1
but product of roots = a - b/b-c = c/a
a-b/b-c = 1
a-b=b-a
2ab =a+c
Hence proved
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