If ^4 + and ^4 + are the roots of the equation x^2+b(2 x+1)=0 and ^2 + and ^2 + are the roots of the equation x^2+4 x+2=0 , then find the value of b where b N . [Note: can be non-real number also.]

Step-by-step solution

aligned ^2 + ^2 +2 & =-4 & = -5 2 ( ^2 + ) ( ^2 + ) & =2 ^2 2 =-7 ^4 + ^4 +2 & =-2 b 1- ^2 2 2 +2 & =-2 b aligned 9+4 =-4 b ...(1) aligned ( ^4 + ) ( ^4 + ) & =b ^4 2 10 + 9 2 + ^2 & =b (4 +5)(4 +17) & =0 aligned If = -5 4 b=-1 (rejected) If = -17 4 b=2