Question

solve the above problem​

Answer 1

Answer:

A ) ( b + c ) = 2a

Step-by-step explanation:

Given-----> If the roots of the equation

( a - b ) x² + ( b - c ) x + ( c - a ) = 0 , are equal .

To find ------> Value of ( b + c ) is .

Solution------> ATQ,

( a - b ) x² + ( b - c ) x + ( c - a ) = 0

Comparing it with Ax² + Bx + C = 0 , we get,

A = ( a - b ) , B = ( b - c ) , C = ( c - a )

ATQ, roots of given equation is equal , so,

B² - 4AC = 0

=> ( b - c )² - 4 ( a - b ) ( c - a ) = 0

=> b² + c² - 2 bc - 4 ( ac - a² - bc + ab ) = 0

=> b² + c² - 2bc - 4ac + 4a² + 4bc - 4ab = 0

=> b² + c² + 4a² - 4ac - 4ab + 2bc = 0

=> b² + c² + ( - 2a )² + 2 ( - 2a ) ( c ) - 2 ( - 2a ) ( b ) + 2bc = 0

We have an identity ,

( p + q + r )² = p² + q² + r² + 2pq + 2qr + 2rp

Applying this identity here , we get,

=> ( b + c - 2a )² = 0

Taking square root of both side , we get,

=> ( b + c - 2a ) = 0

=> b + c = 2a