Question

`(t - 9)^(1/2) - t^(1/2) = 3?`solve the radical equations, if possible.

Answer 1

No solution

Explanation:

Given: `(t-9)^(1/2) - t^(1/2) = 3 " or " sqrt(t-9) - sqrt(t) = 3`

Add the `sqrt(t)` to both sides of the equation:

`sqrt(t-9) - sqrt(t) + sqrt(t) = 3 + sqrt(t)`

Simplify: `sqrt(t-9) = 3 + sqrt(t)`

Square both sides of the equation:

`(sqrt(t-9))^2 = (3 + sqrt(t))^2`

`t - 9 = (3 + sqrt(t)) ( 3 + sqrt(t))`

Distribute the right side of the equation:

`t - 9 = 9 + 3 sqrt(t) + 3 sqrt(t) + sqrt(t)sqrt(t)`

Simplify by adding like terms and using `sqrt(m) sqrt(m) = sqrt(m*m) = sqrt(m^2) = m`:

`t - 9 = 9 +6 sqrt(t) + t`

Subtract `t` from both sides:

`- 9 = 9 +6 sqrt(t)`

Subtract `-9` from both sides:

`-18 = 6 sqrt(t)`

Divide both sides by `6`:

`-3 = sqrt(t)`

Square both sides:

`(-3)^2 = (sqrt(t))^2`

`t = 9`

Check:
Always check your answer for radical problems by putting it back into the original equation to see if it works:

`sqrt(9-9) - sqrt(9) = 0 - 3 = -3 != 3`

No solution