SOLUTION: The product of two positive numbers is 1 and their difference is 3/2. Find the larger number. PLEASE explain how to do it???

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Question 209910: The product of two positive numbers is 1 and their difference is 3/2. Find the larger number. PLEASE explain how to do it???
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = the larger number and b = the smaller number.
a%2Ab+=+1 and...
a-b+=+3%2F2 Rewrite this as a+=+b%2B3%2F2 and substitute into the first equation.
%28b%2B3%2F2%29%2Ab+=+1 Simplify.
b%5E2%2B%283%2F2%29b+=+1 Subtract 1 from both sides.
b%5E2%2B%283%2F2%29b-1+=+0 Multiply through by 2 to clear the fraction.
2b%5E2%2B3b-2+=+0 Factor this trinomial.
%282b-1%29%28b%2B2%29+=+0 Apply the zero product rule.
2b-1+=+0 or b%2B2+=+0 so that...
2b+=+1 or b+=+-2 Discard the negative solution as the numbers are to be positive.
2b+=+1 Divide both sides by 2.
b+=+1%2F2 This is the smaller number.
a+=+b%2B3%2F2 Substitute b = 1/2.
a+=+1%2F2+%2B+3%2F2
highlight%28b+=+2%29 This is the larger number.
Check:
a%2Ab+=+%282%29%2A%281%2F2%29
a%2Ab+=+1 and...
a-b+=+2-1%2F2
a-b+=+3%2F2