Question

64 POINT QUESTION

√(5-2x) - √(2-x) = 1

Answer 1

x = 2 and x = -2

Explanation:

The easiest way is to guess. We know that you can't have a square root of a negative number. This constrains x between negative infinity to 2. Testing 2 and -2, we see that it satisfy the equation.

The more systematic approach is shown below

`√(5-2x)-√(2-x)=1 \\√(5-2x)-√(2-x)+√(2-x)=1+√(2-x) \\√(5-2x) = 1+√(2-x)`

`5-2x=(1+√(2-x))^2\\5-2x=1+2√(2-x)+2-x\\2-x=2√(2-x)\\1-0.5x=√(2-x)\\(1-0.5x)^2=2-x\\1-x+0.25x^2=2-x\\0.25x^2-1=0\\0.25x^2 = 1\\x^2 = 4\\x = +/-2`

x= -2, 2