Question

Question #5a496

Answer 1

No real solutions.

Explanation:

We have: `y = sqrt(x - 1) + 2`

Let's set `y` equal to zero:

`Rightarrow y = 0`

`Rightarrow sqrt(x - 1) + 2 - 0`

Subtracting `2` from both sides of the equation:

`Rightarrow sqrt(x - 1) = - 2`

Squaring both sides:

`Rightarrow (sqrt(x - 1))^(2) = (- 2)^(2)`

`Rightarrow x - 1 = 4`

Adding `1` to both sides:

`therefore x = 5`

Let's verify if this value of `x` works in the original equation:

`Rightarrow sqrt(x - 1) + 2 - 0`

`Rightarrow sqrt((5) - 1) + 2 = 0`

`Rightarrow sqrt(4) + 2 = 0`

`Rightarrow 2 + 2 = 0`

`Rightarrow 4 ne 0`

Therefore, there are no real solutions to the equation.