Radicals
Solve:
√x+2 + √x-1=2
To solve this equation, we need to isolate the square roots on one side of the equation and then square both sides to eliminate the square roots.
Given equation: √x+2 + √x-1 = 2
Subtract √x-1 from both sides:
√x+2 = 2 - √x-1
Now, square both sides:
(√x+2)^2 = (2 - √x-1)^2
x + 2√x + 4 = 4 - 4√x + x - 1
x + 2√x + 4 = 3 - 4√x
Rearranging terms:
x + 4√x - 4√x - x = 3 - 4
x = -1
Therefore, the solution to the equation √x+2 + √x-1 = 2 is x = -1.