Question

What is the solution to the equation sqrt(x^2+2x-25)=sqrt(x+5)?

Answer 1

We have to decide if the square root is the radical sign, meaning the principal square root, or a multivalued square root.

Let's assume this is the radical sign applied to the radicands, indicating both sides are the principal square root.

`√(x^2 + 2x - 25)= √(x+5)`

In this case, dealing with the principal values, it's ok to square both sides. Both sides are positive (or a positive number times i); we won't introduce extraneous roots.

`x^2 + 2x - 25 = x+5`

`x^2+ x -30 = 0`

`(x-5)(x+6)=0`

Answer: x=5 or x=-6

Check:

`√(5^2+2(5)-25)=√(10)`

`√(5+5)=√(10) \quad\checkmark`

`√((-6)^2 + 2(-6) - 25) = √(-1) = i`

`√(-6+5)=√(-1)=i \quad\checkmark`

I suppose it depends what grade you're in as to whether you'll accept x=6 as a solution.

Answer (restricting ourselves to real square roots): x=5

Answer 2

Answer: x=5 on edge

Explanation:

I tried x= -6, x= 5 and it was incorrect.