If h x= sech y= 3 5 and e^ x + y is an integer, then e^ x + y =

Step-by-step solution

aligned & h x= 3 5 e^x-e^ -x e^x+e^ -x = 3 5 e^ 2 x -1 e^ 2 x +1 = 3 5 & 5 e^ 2 x -5=3 e^ 2 x +1 e^ 2 x =4 e^x=2 & And, h y= 3 5 2 e^y+e^ -y = 3 5 2 e^y e^ 2 y +1 = 3 5 & 10 t=3 t^2+3 & [ Let e^y=t ] & 3 t^2-10 t+3=0 t=3, 1 3 e^y=3, 1 3 aligned So, e^ x+y =e^x e^y=2 3=6 .