SOLUTION: Please help!!! 3y-2 (inside radical)= y-2

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Question 264730: Please help!!!
3y-2 (inside radical)= y-2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%283y-2%29=y-2 Start with the given equation.


3y-2=%28y-2%29%5E2 Square both sides to eliminate the square root.


3y-2=y%5E2-4y%2B4 FOIL


0=y%5E2-4y%2B4-3y%2B2 Get all terms to one side.


0=y%5E2-7y%2B6 Combine like terms.


Notice that the quadratic y%5E2-7y%2B6 is in the form of Ay%5E2%2BBy%2BC where A=1, B=-7, and C=6


Let's use the quadratic formula to solve for "y":


y+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


y+=+%28-%28-7%29+%2B-+sqrt%28+%28-7%29%5E2-4%281%29%286%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-7, and C=6


y+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%281%29%286%29+%29%29%2F%282%281%29%29 Negate -7 to get 7.


y+=+%287+%2B-+sqrt%28+49-4%281%29%286%29+%29%29%2F%282%281%29%29 Square -7 to get 49.


y+=+%287+%2B-+sqrt%28+49-24+%29%29%2F%282%281%29%29 Multiply 4%281%29%286%29 to get 24


y+=+%287+%2B-+sqrt%28+25+%29%29%2F%282%281%29%29 Subtract 24 from 49 to get 25


y+=+%287+%2B-+sqrt%28+25+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


y+=+%287+%2B-+5%29%2F%282%29 Take the square root of 25 to get 5.


y+=+%287+%2B+5%29%2F%282%29 or y+=+%287+-+5%29%2F%282%29 Break up the expression.


y+=+%2812%29%2F%282%29 or y+=++%282%29%2F%282%29 Combine like terms.


y+=+6 or y+=+1 Simplify.


So the possible solutions are y+=+6 or y+=+1


However, we need to check them. To do that, simply plug each possible solution into sqrt%283y-2%29=y-2. If you get a true equation, then it will verify that particular possible solution. I'll let you do the check. Hint: One of the "possible" solutions is not a solution at all.