SOLUTION: Please help Solve: (sqrt of 2x - 3) = x - 1 Solve: (sqrt of 3x - 3) - (sqrt of x) = 1

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Question 728593: Please help
Solve: (sqrt of 2x - 3) = x - 1

Solve: (sqrt of 3x - 3) - (sqrt of x) = 1

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%282x+-+3%29+=+x+-+1....square both sides
%28sqrt%282x+-+3%29%29%5E2+=+%28x+-+1%29%5E2
2x+-+3+=+x%5E2-2x+%2B1
0=+x%5E2-2x-2x%2B3+%2B1
0=+x%5E2-4x%2B4...use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A4+%29%29%2F%282%2A1%29+
x+=+%284+%2B-+sqrt%28+16-16+%29%29%2F2+
x+=+%284+%2B-+sqrt%28+0+%29%29%2F2+
x+=+%284+%2B-+0%29%2F2+
so, solution is
x+=+4%2F2+
x+=+2+

choice: (c.) 2


sqrt%283x-3%29+-+sqrt%28x%29+=+1
sqrt%283x-3%29++=+sqrt%28x%29%2B1...square both sides
%28sqrt%283x-3%29%29%5E2+=+%28sqrt%28x%29%2B1%29%5E2
3x-3+=x%2B2sqrt%28x%29%2B1
3x-x-3-1+=2sqrt%28x%29
2x-4+=2sqrt%28x%29
2%28x-2%29+=2sqrt%28x%29
cross%282%29%28x-2%29+=cross%282%29sqrt%28x%29
x-2+=sqrt%28x%29..square both sides again
%28x-2%29%5E2+=%28sqrt%28x%29%29%5E2
x%5E2-4x%2B4+=x

x%5E2-4x-x%2B4+=0
x%5E2-5x%2B4+=0

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-5%29+%2B-+sqrt%28%28-5%29%5E2-4%2A1%2A4+%29%29%2F%282%2A1%29+

x+=+%285+%2B-+sqrt%2825-16+%29%29%2F2+
x+=+%285+%2B-+sqrt%289+%29%29%2F2+

x+=+%285+%2B-+3%29%2F2+
solutions:
x+=+%285+%2B3%29%2F2+
x+=+8%2F2+
x+=+4+
and
x+=+%285+-3%29%2F2+
x+=+2%2F2+
x+=+1+

choice: (c.) 1 and 4