How do you work out the radical eqaution? and what is the restriction?

This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)
Expert Answers
embizze eNotes educator| Certified Educator


As for most equations, we try to isolate the variable by using inverse operations.

Subtract 1 from each side:


Square both sides -- be aware that squaring both sides of an equation can lead to extraneous solutions.


Multiply both sides of the equation by 3/7:


Check the answer in the original equation. (This must be done in order to check if we have introduced an extraneous solution.)

`1+sqrt((7*21)/3)=1+sqrt(49)=8` as required.

Note that `sqrt((7x)/3)` is only defined in the reals if the argument is nonnegative; so `x>=0` .``


The solution is x=21. The expression on the left side of the equation is only defined in the reals for x nonnegative.


The graph of the left and right side expressions: