SOLUTION: Please help! I have no idea how to even approach this problem. Thank you. One on one. Find two positive real numbers that differ by 1 and have a product of 1.

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Question 61086This question is from textbook
: Please help! I have no idea how to even approach this problem. Thank you. One on one. Find two positive real numbers that differ by 1 and have a product of 1. This question is from textbook

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Help Please! Find the exact an approximate solution. Find two positive real numbers that differ by one and have a product of one.
LET ONE NUMBER = X
OTHER NUMBER = X-1
PRODUCT = X(X-1)=1
X^2-X=1
X^2-X-1=0.....COMPARING WITH AX^2+BX+C=0...A=1...B=-1....C=-1
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+
x+=+%281+%2B-+sqrt%28+1%2B4+%29%29%2F%282%29+
x+=+%281+%2B-+sqrt%28+5+%29%29%2F%282%29+
SINCE POSITIVE NUMBERS ARE ASKED FOR THEY ARE
[1+SQRT(5)]/2 AND [1+SQRT(5)]/2 -1..OR ....[SQRT(5)-1]/2