Question

Radical equation? 3-square root of x+1= square root of x-2

How to solve step by step

Answer 1

There's a few ways to interpret what you wrote so I'll explore two of the most likely:

SIMPLEST
`3-sqrt(x)+1 = sqrt(x) - 2`
The squareroots can be combined and the equations simplified to find
`6 = 2sqrt(x) implies 3 = sqrt(x) implies x = 9`

MORE COMPLEX
`3 - sqrt(x+1) = sqrt(x-2) implies sqrt(x-2) + sqrt(x+1) = 3`

There isn't an easy, general way to solve equations like this. Here, we can only observe that the two numbers under the square roots are 3 apart. The only squares that are three apart are 4 and 1, which work (since `sqrt(1) + sqrt(4) = 3`) Therefore,

`x-2 = 1 implies x = 3` is a solution that works.