If the equation |2 x+ ^2 a |+|2 x+3+2 a|=0 has exactly one solution x= (where ' a ' is a constant) then find the value of 4 ^2 .

Step-by-step solution

array rlrlrl & |2 x+ ^2 a |+|2 x+3+2 a| & =0 & & & 2 x+ ^2 a & =0 & and & 2 x+3+2 a & =0 Hence, & ^2 a-2 a-3 & =0 & & a=-1 & 2 x & =-1 & & & x= =-1 / 2 & 4 ^2 & =1 & & & array