If the roots of equation (b-c)x*+(c-a)x+(a-b)=0 then prove that 2b=a+c

1.	If the roots of equation (b-c)x*+(c-a)x+(a-b)=0 then prove that 2b=a+c
Answer» Given, the\xa0roots of the equation (b - c)x2\xa0+ (c - a)x + (a - b) = 0 are equal.Hence,\xa0{tex}D = 0{/tex}{tex}\\Rightarrow{/tex}{tex}( c - a )^2\xa0-\xa04( b - c )( a - b ) = 0{/tex}{tex}\\Rightarrow{/tex}{tex}c^2 + a^2 + 4b^2 - 2ac - 4ab + 4ac - 4bc\xa0= 0{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}(c + a - 2b)^2 = 0{/tex}{tex}\\Rightarrow{/tex}{tex}\xa0c + a - 2b = 0{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}2b = a + c{/tex}

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