Question

The square root of 1 less than twice a number is equal to 2 less than the number.Find the number.

Answer 1

I read that as:
√(2x - 1) = x-2

square both sides
2x-1 = x^2 - 4x + 4
x^2 - 6x + 5 = 0
(x-5)(x-1) = 0
x = 5 or x = 1

since I squared, both answers must be verified in the original equation,

if x = 1
LS = √(2x-1) = √1 = 1
RS = 1-2 = -1
so x ≠ 1

if x = 5
LS = √(10-1) = 3
RS = 5-2 = 3

your number is 5