the least value of 'a' for which the equation `2sqrt(a) sin^(2) x+sqrt(a-3) sin 2x=5+sqrt(a)` has at least one solution is _______.

Answer

14

Explanation

We have `sqrt(a-3) sin 2x - sqrt(a) (1-2 sin^(2) x)=5`
`:. sqrt(a-3) sin 2x-sqrt(a) cos 2x =5`
This equation has at least one solution if
`5 le sqrt((sqrt(a-3))^(2)+(sqrt(2))^(2))`
or `2a-3 ge 25`
`:. a ge 14`
So, least value of a is 14.