Can someone help me solve this and break it down step by step please???
[Sqrt(x-3)]-[Sqrt(x+2)]=3
take the one root to the other side
√(x-3) = 3 + √(x+2)
square both sides
x - 3 = 9 + 6√(x+2) + x + 2
-14 = 6√(x+2)
At this point I can see there is no solution, since the root sign means to take the positive square root of a number.
Intuitively we can see that from the opening equation.
since x+2 > x-3
then the square root of x+2 > square root of x-3
and their difference the way it is written would have to be a negative number.