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We know that.,,
If the quadratic equation ax^2+bx+c=0, whose roots are equal then its determinant is equal to 0.
> (a-b)x^2+(b-c)x+(c-a)=0
Determinant =0,,
Now
> (b-c)^2-4(a-b)(c-a)=0
> b^2+c^2-2bc-4ac+4a^2+4bc-4ab=0
> b^2+c^2+(-2a)^2+2bc+2c(-2a)+2(-2a)b=0
> (b+c-2a)^2=0
> b+c-2a=0
therefore,,,
b+c=2a
So,,, 2a=b+c
Proved..........
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