How do I get the roots from this equation?

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- October 19th 2012, 04:15 AMJason76Solving a Two Radical Equation for Roots
How do I get the roots from this equation?

- October 19th 2012, 04:24 AMTheEmptySetRe: Solving a Two Radical Equation for Roots
- October 19th 2012, 04:33 AMJason76Re: Solving a Two Radical Equation for Roots
I basically get the jist of it but I don't understand the following line:

So

was squared (to get rid of the square root), so now the same has to be done to the other side. However,

(to the right of the equation)

was not under square root. So why was it squared?

Obviously,

was squared to get rid of the radical sign. - October 19th 2012, 04:41 AMTheEmptySetRe: Solving a Two Radical Equation for Roots
- October 19th 2012, 04:58 AMJason76Re: Solving a Two Radical Equation for Roots
Considering again:

Right, but

is a binomial, yet, after squaring, no distributive property is used on it. On the other hand,

(after squaring) gets a distributive property operation done to it. Plus, I don't understand where the

really came from.

Again:

Anyhow, what I'm trying to say is "Two binomials exist on both sides of the equation. Both of them should be squared (to get rid of the radical signs). Therefore, the binomial on the left is squared, as expected. However, the one on the right is different. It is squared and then distributed. Yet, the radical sign remains for one of the duplicate terms.". Plus, I still have no idea where the

came from. I'm assuming the came from squaring. - October 19th 2012, 06:43 PMJason76Re: Solving a Two Radical Equation for Roots
Sorry to bump thread, but I couldn't edit the last post.

Here is what I'm saying more clearly:

How do I solve this for roots?

Put one radical on the right side of the equation.

Square both sides to get rid of radicals.

Squaring both sides (to get rid of radicals) should lead to this (by my logic):

But this is the correct answer (according to the book):

That's main part I have trouble with. The rest is easy to understand.

Of course, this only half of the problem. I haven't solved for roots yet. - October 19th 2012, 06:53 PMMarkFLRe: Solving a Two Radical Equation for Roots
Look at the rule

**TheEmptySet**gave in post #4...this will tell you why the squaring of the side in question becomes what it does. - October 20th 2012, 06:22 AMJason76Re: Solving a Two Radical Equation for Roots
I think I got it now:

Recognize it (right hand side of equation) as a "Square of a Binomial".

FOIL

Next, add the two middle terms. In this case, it's adding negatives, so it's -b - b. The same as -b (+) -b

Full equation:

Next, more algebra until the roots are found. - October 20th 2012, 07:57 PMJason76Re: Solving a Two Radical Equation for Roots
Ok. Here is the 2nd part of the equation:

Isolate the radical again by moving it to the left side.

Turn this into a quadratic equation by creating a 0 on one side.

(one linear factor):

Roots:

or

Plugin those values into the original equation to see if each one is true.

One question. Where did the 0 come from? - October 20th 2012, 10:14 PMearbothRe: Solving a Two Radical Equation for Roots