(b, c)

The given equation is, π e (x– π ) (x– π –e) + e π (x –e) (x – π – e) + ( π π + e e ) (x – e) (x – π ) = 0

Let f(x) = π e (x – π ) (x – π – e) + e π (x – e)

(x – π – e) + ( π π + e e ) (x – e) (x – π )

Then f(e) = π e (e – π ) (– π ) > 0 [  e < π ] and f( π ) = e π ( π – e)

(– e) < 0

Equation f(x) = 0 has a real root in (e, π ).

Again f( π + e) = ( π π + e e ) ( π ) (e) > 0

∴ Equation f(x) = 0 has a real root in ( π , e + π )

∴ f(x) = 0 has a real roots in (e, π ) and other in ( π , π + e)

Also, π – e < e

∴ Equation f(x) = 0 has two real roots in ( π – e, π + e)