SOLUTION: Solve each of the equations. Be sure to check your solutions. √2y + 7+ 4=y (The radical symbol is over the 2y+7)

Algebra ->  Radicals -> SOLUTION: Solve each of the equations. Be sure to check your solutions. √2y + 7+ 4=y (The radical symbol is over the 2y+7)      Log On


   

Question 78525: Solve each of the equations. Be sure to check your solutions.
√2y + 7+ 4=y
(The radical symbol is over the 2y+7)
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28%282%2Ay%29%2B7%29%2B4=y
First, get the terms under the radical on one side of the equation:
sqrt%28%282%2Ay%29%2B7%29=y-4
Now, square both sides of the equation:
%282%2Ay%29%2B7=%28y-4%29%5E2
Simplify, and put the equation into ax%5E2%2Bbx%2Bc=0 form:
%282%2Ay%29%2B7=y%5E2-%288%2Ay%29%2B16
y%5E2-%2810%2Ay%29%2B9=0
Factor this expression as follows:
%28y-1%29%2A%28y-9%29=0
Note that this is a second order equation, so there are two roots.
Equate each of the factors you just found to zero and solve for y.
You get:
y=1 and y=9
Now, this part is important... you need to plug these answers
back in to the original problem to be sure they are not "extraneous."
An extraneous root is mathematically corrrect, but not a true answer.
If you plug y=1 back into the original equation, you will see that the
equation does NOT hold. Hence this is an extraneous root.
If you plug y=9 back into the original equation, you will see that the
equation DOES hold. so that one is your answer.