SOLUTION: A student is asked to solve b^2+b^2=c^2 for a and gives the following solution. Assume all variables represent positive Real Numbers.
(Step 1) {{{ b^2+a^2=c^2 }}}
(Step
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-> SOLUTION: A student is asked to solve b^2+b^2=c^2 for a and gives the following solution. Assume all variables represent positive Real Numbers.
(Step 1) {{{ b^2+a^2=c^2 }}}
(Step
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Question 964233: A student is asked to solve b^2+b^2=c^2 for a and gives the following solution. Assume all variables represent positive Real Numbers.
(Step 1)
(Step 2)
(Step 3) b+a=c
(Step 4) a=c-b
Explain the mistake(s) made by the student and provide the correct solution. Make sure to analyze the entire solution as there may be multiple mistakes made.
I cannot figure out the answers to this question. I think I might have the answers but I am not sure they are correct. Any help would be appreciated! Found 2 solutions by Alan3354, Edwin McCravy:Answer by Alan3354(69443) (Show Source):
A student is asked to solve b^2+a^2=c^2 for a and gives the following
solution. Assume all variables represent positive Real Numbers.
(Step 1)
(Step 2)
(Step 3) b+a=c
That step is wrong. This mistake is trying to use a rule that applies
only to MULTIPLIED quantities under a square root radical for ADDED
quantities under a radical. If b2a2 had been under the radical and we had
had that would have given but since b2 and a2 are added under
the radical the rule doesn't work. So step (3) should be:
We cannot take ADDED squared terms from under a square root radical individually
like we can MULTIPLIED squared terms under a square root radical. So we have
to leave the problem like that.
Edwin
