SOLUTION: Solve: X= sqr rt x-1 + 3

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Question 201519: Solve: X= sqr rt x-1 + 3
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
x+=+sqrt%28x-1%29%2B3 First, subtract 3 from both sides of the equation.
x-3+=+sqrt%28x-1%29 Next, square both sides. Note that you may introduce an extraneous root when you square both sides so you must check your solutions to confirm their validity.
%28x-3%29%5E2+=+x-1 Simplify the left side.
x%5E2-6x%2B9+=+x-1 Subtract x from both sides.
x%5E2-7x%2B9+=+-1 Now add 1 to both sides.
x%5E2-7x%2B10+=+0 Solve this quadratic equation by factoring.
%28x-2%29%28x-5%29+=+0 Apply the zero product rule.
x-2+=+0 or x-5+=+0 so that...
highlight_green%28x+=+2%29 or highlight_green%28x+=+5%29
Check the solutions:
x+=+sqrt%28x-1%29%2B3 Substitute x = 2.
2+=+sqrt%282-1%29%2B3
2+=+sqrt%281%29%2B3 Note that sqrt%281%29+=+1 or sqrt%281%29+=+-1
2+=+1%2B3 or 2+=+-1%2B3
highlight%282+%3C%3E+4%29 or highlight_green%282+=+2%29 ...and for the other solution...
x+=+sqrt%28x-1%29%2B3 Substitute x = 5
5+=+sqrt%285-1%29%2B3
5+=+sqrt%284%29%2B3
5+=+2%2B3 or 5+=+-2%2B3
highlight_green%285+=+5%29 or highlight%285+%3C%3E+1%29