SOLUTION: sqrt(4x+1)-sqrt(x-1)=2

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Question 991000: sqrt(4x+1)-sqrt(x-1)=2
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%284x%2B1%29-sqrt%28x-1%29=2

sqrt%284x%2B1%29=sqrt%28x-1%29%2B2
4x%2B1=x-1%2B4sqrt%28x-1%29%2B4
4x-x%2B1%2B1-4=4sqrt%28x-1%29
3x-4=4sqrt%28x-1%29
9x%5E2-24x%2B16=16%28x-1%29
9x%5E2-24x%2B16-16x%2B16=0
9x%5E2-40x%2B32=0

x=%2840%2B-+sqrt%281600-4%2A9%2832%29%29%29%2F%282%2A9%29

x=%2840%2B-+sqrt%28448%29%29%2F%282%2A9%29

x=%2840%2B-+sqrt%2816%2A28%29%29%2F%282%2A9%29

x=40%2F2%2B-+%284%2F2%29%281%2F9%29sqrt%2828%29

x=20%2B-+%282%2F9%29sqrt%2828%29

highlight%28x=20%2B-+%284%2F9%29sqrt%287%29%29

Check the minus-form carefully.
x=20-%284%2F9%292.646
x=18.824, approximation. This will work, as well as the plus-form.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt(4x+1)-sqrt(x-1)=2
highlight_green%28system%28x+=+2_or%2Cx+=+10%2F9%29%29