Find the number of solution of the equation 2^ ^2 x +5 2^ ^2 x =7 in the interval [0,315] .

Step-by-step solution

aligned & 2^ ^2 x +5 2^ ^2 x =7 & 2^ ^2 x +5 2^ 1- ^2 x =7 & 2^ ^2 x =t t+ 10 t =7 aligned aligned & t^2-7 t+10=0 (t-5)(t-2)=0 t=2 or 5 & t=2^ ^2 x =2 or 5 aligned but 2^ ^2 x 5 (think !) 2^ ^2 x =2=2^1 ^2 x=1 Hence values of x in [0,315] is 2 , 3 2 , 5 2 , . 199 2 total number of solution in [0,315] is 100