Solve the equation
`sqrt((2x^(2)+5x-2))-sqrt(2x^(2)-5x-9)=1`

Explanation

Let `u=sqrt((2x^(2)+5x-2))`
and `v=sqrt((2x^(2)+5x-2))`
`:.u^(2)=2x^(2)+5x-2`
and `v^(2)=2x^(2)+5x-9`
Then the give equation reduces to the solution of the system of algebraic equations.
`u-v-1`
`u^(2)-v^(2)=7`
`implies(u+v)(u-v)=7`
`impliesu+v=7 [ :' u-v=1]`
We get `u=4,v=3`
`:.sqrt(2x^(2)-5x-2)=4`
`:.2x^(2)+5x-18=0`
`:.x_(1)=2` and `x_(2)=-9//2`
Both roots satisfies the original equation.
Hencce `x_(1)=2` and `x_(2)=9//2` are the roots of the original equation.