Radical Equation Without Constant

[mathdad]

Solve for all real number t values.

sqrt {2t + 5} - sqrt {8t + 25} + sqrt {2t + 8} = 0

I see there are no constants in this problem. I typically isolate the radical on one side of the equation and the constant (s) on the other side but there are 3 radicals on the left side. This is strange.

Can someone get me started?

 

[Greg]

Rewrite as $\sqrt{2t+5}+\sqrt{2t+8}=\sqrt{8t+25}$. What do you get when you square both sides?

 

[mathdad]

Rewrite as $\sqrt{2t+5}+\sqrt{2t+8}=\sqrt{8t+25}$. What do you get when you square both sides?

I had no idea that it is legal to move one radical over to the other side. When I square both sides, the radicals go away.

 

[topsquark]

I had no idea that it is legal to move one radical over to the other side. When I square both sides, the radicals go away.

At a guess you are forgetting about the cross term. \(\displaystyle (a + b)^2 \neq a^2 + b^2\). It is \(\displaystyle (a + b)^2 = a^2 + 2ab + b^2\). You are going to end up having to apply getting rid of the radicals two times. For each one you pick a term and put it on the RHS. Then square it.

-Dan

 

[mathdad]

Very good. I will work on this later.