Isolate one of the square root terms, it doesn't matter which one.
I'll isolate the first one:
Square both sides:
Square each factor on the left. Copy the binomial on the right
twice and multiply using FOIL:
It will make things easier to divide each term by 2
Isolate the square root term on the right:
Divide through by -1
It will make things easier to divide each term by 3
Square both sides:
Divide through by 4
Checking x=5 in the original equation:
That checks.
Checking x=79.75 in the original equation
[That gives us 85, and so 79.75 is an extraneous solution.
It is interesting that extraneous solutions usually would
have checked if one of the square root terms could have
its sign changed in front. We see here that if the 31 had
been -31, we'd have had -31+54=23, which would have checked.
This is due to the fact that when we square a negative number,
we get the same thing as when we square the corresponding
positive number. We squared both sides twice, so we should
expect that.]
There is only one solution x=5.
Edwin
