Question

if x/b+b/x=a/b+b/a find the roots of the equation​

Answer 1

Answer:

"Solve 1/x + a - 1/ x + b = 1/a - 1/b

Solution: Determine whether this equation reduces to the quadratic form. The given equation is ( x + b ) - ( x + a ) / ( x + a ) ( x + b ) = ( b - a )/ab i.e., ( b - a ) / ( x + a ) ( x + b ) = ( b - a ) / ab ( x + a ) ( x + b ) = ab i.e., x2 + ( a + b ) x + ab = ab Therefore, x2 + ( a + b ) x = 0 i.e., x ( x + ( a + b ) ) = 0 i.e., x = 0 or x + ( a + b ) = 0 i.e., x = 0 or x = - ( a + b ) Solution set = { 0, - ( a + b ) }"

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