Solve the inequation
`-|y|+x-sqrt((x^(2)+y^(2)-1))ge1`

Explanation

We have `-|y|+x-sqrt((x^(2)+y^(2)-1))ge1`
`impliesx-|y+ge1+sqrt((x^(2)+y^(2)-1))`
if `xge|y|`
then squaring both sides
`x^(2)+y^(2)-2x|y|ge1+x^(2)+y^(2)-1+2sqrt((x^(2)+y^(2)-1))`
`implies-x|y|gesqrt((x^(2)+y^(2)-1))` ………..i
Since `x ge|y|ge0`............ii
Then LHS of Eq. (i) is non -positive and RHS of Eq. ii is non negative Therefore the system is satisfied only whe both sides are zero.
`:.`The inequality Eq i is equivalent to the system
`{(x|y|=0),(x^(2)+y^(2)-1=0):}`
the eq i gives `x=0` or `y=0`. If `x=0` then we find `y=+-1`
from eq. ii but `xge|y|` which is impossible.
If `y=0`, then from eq ii we find
`x^(2)=1`
`:.x=1,-1`
Taking `x=1 [:' xge|y|]`
`:.` The pair (1,0) satisfies the given inequation. HEnce (1,0) is the solution of the original inequation.