SOLUTION: solve the following equations or system of equations 1 + √5-x = x-2

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Question 140712This question is from textbook
: solve the following equations or system of equations
1 + √5-x = x-2 This question is from textbook

Answer by solver91311(24713) About Me  (Show Source):
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I think you mean 1+%2B+sqrt%285-x%29=x-2 (if so, next time construct it like this 1 + sqrt(5 - x) = x - 2)

Add -1 to both sides:

sqrt%285-x%29=x-3

Square both sides (this introduces the possibility of an extraneous root -- check your answers carefully)

5-x=%28x-3%29%5E2
5-x=x%5E2-6x%2B9
-x%5E2%2B6x-x-9%2B5=0
-x%5E2%2B5x-4=0
x%5E2-5x%2B4=0

Solve by any method. Remember to check for and exclude extraneous roots.

Hint: sqrt%284%29=2%3C%3E-2, -sqrt%284%29=-2