If x+ ^2 x=1, x (0, 2 ) , then ( ¹² x+ ¹² x )+3 ( ¹⁰ x+ ¹⁰ x+ ^8 x+ ^8 x )+ ( ^6 x+ ^6 x ) is equal to :

Step-by-step solution

aligned & x+ ^2 x=1 & x= ^2 x x= x aligned Given expression aligned & =2 ¹² x+6 [ ¹⁰ x+ ^8 x ]+2 ^6 x & =2 [ ^6 x+3 ^5 x+3 ^4 x+ ^3 x ] & =2 ^3 x [( x+1)^3 ] & =2 [ ^2 x+ x ]^3 & =2 aligned