SOLUTION: If 5 times a number is decreased by 4 the principal root of this difference is 2 less than the number find the numbers

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Question 657890: If 5 times a number is decreased by 4 the principal root of this difference is 2 less than the number find the numbers
Answer by kevwill(135) About Me  (Show Source):
You can put this solution on YOUR website!
If I'm reading the problem statement correctly, we are to find x such that
sqrt%285x+-+4%29+=+x+-+2
Squaring both sides:
5x+-+4+=+x%5E2+-+4x+%2B+4
x%5E2+-+4x+%2B+4+-+%285x+-+4%29+=+0
x%5E2+-9x+%2B+8
We can solve for x using the quadratic equation x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ with a=1, b=-9, and c=8:
x+=+%28-%28-9%29+%2B-+sqrt%28+%28-9%29%5E2-4%2A1%2A8+%29%29%2F%282%2A1%29+
x+=+%289+%2B-+sqrt%28+81-32+%29%29%2F2+
x+=+%289+%2B-+sqrt%28+49+%29%29%2F2+
x+=+%289+%2B-+7%29%2F2+
So x = 1 or x = 8. However x cannot be 1 because we are told that the principle root of 5x-4 = x-2, but x-2 = -1, so we would not be taking the principle root.
Hence, x = 8.