6. Equations With Radicals

It is important in this section to check your solutions in the original equation, as we often produce solutions which actually don't work when subsituted back into the original equation.

(In fact, it is always good to check solutions for equations - you learn so much more about why things are working the way they do. ^_^)

 

Example:

Solve math expression

Answer

Squaring both sides gives:

math expression

So our solutions are x = 1.5 or -1.

CHECK:

Substituting x = 1.5 in our original equation gives:

math expression

Checks OK

Substituting x = -1 in our original equation gives:

math expression

DOES NOT check OK

So we conclude the only solution is x = 1.5.

Can you figure out where the 'wrong' solution is coming from?

 

Exercises

1. Solvemath expression


Answer

2. Solvemath expression


Answer

3. Solvemath expression


Answer

4. In the study of spur gears in contact, the equation

math expression

is used. Solve for math expression.


Answer



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