Please help me solve:

Question

[SQRT(x)]=-2
1.
[SQRT(2x2 - 1)]=x

Answer 1

[SQRT(x)]=-2
has no solution since by definition √ gives only positive result.

for verification graph f(x) = √x + 2
it never touches or crosses the x-axis

for the second, I assume you mean
√(2x^2-1) = x
square both sides
2x^2-1 = x^2
x^2 = 1
x = ±1
but since we squared, both answers must be verfied.
if x=1
LS = √(2-1) = 1
RS = 1, so it works

if x=-1
LS = √(2-1) = 1
RS = -1 , does not work

so x = 1