Trouble Solving an Equation that has square roots on both sides

In summary, the conversation was about solving an equation for C. The equation involved square roots on both sides, and the person was unsure of how to eliminate them. After some calculations, the equation was simplified into a quadratic form.
  • #1
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Hey all,
I am having trouble solving the following equation for C
$$A(-\sqrt{C^2+4F_{+}}-C) = B(\sqrt{C^2+4F_{-}}+C)$$
I don't know how to get ride of the square roots on both sides.
Any help would be appreciated, thanks!
 
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  • #2
\begin{align*}
\sqrt{C^2+4F_{+}}&=D\sqrt{C^2+4F_{-}}+EC\\
C^2+4F_{+}&=D^2\left(C^2+4F_{-}\right)+E^2C^2+2DEC\sqrt{C^2+4F_{-}}\\
GC^2+H&=C\sqrt{C^2+4F_{-}}\\
G^2C^4+H^2+2GHC^2&=C^2(C^2+4F_{-})\\
\alpha C^4 + \beta C^2 +\gamma &=0
\end{align*}

Looks like some work to do because of the many constants, but doable.
 
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1. How do I solve an equation with square roots on both sides?

To solve an equation with square roots on both sides, you need to isolate the square root terms on one side of the equation. Then, you can square both sides of the equation to eliminate the square roots and solve for the variable.

2. Can I just square the entire equation to get rid of the square roots?

No, you cannot square the entire equation. You must square each individual term on both sides of the equation to eliminate the square roots. Remember to distribute the square to each term within parentheses.

3. What happens if there are other terms in the equation besides the square roots?

If there are other terms in the equation, you must first isolate the square root terms on one side of the equation. Then, you can square both sides to eliminate the square roots and solve for the variable. Be careful to distribute the square to each term within parentheses.

4. Are there any special rules for solving equations with square roots on both sides?

Yes, there are a few special rules to keep in mind when solving equations with square roots on both sides. First, remember to always check your solutions to make sure they are valid. Also, be careful when squaring both sides of the equation, as this can introduce extraneous solutions.

5. Is there a faster or easier way to solve equations with square roots on both sides?

There is no faster or easier way to solve equations with square roots on both sides. The process of isolating and squaring terms on both sides is necessary to eliminate the square roots and solve for the variable. However, with practice and familiarity, this process can become easier and more efficient.

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