SOLUTION: instruction: find exact & approximate solutions to the problem. 106. One on One. Find two positive real numbers that differ by 1 and have a product of 1.

Question 36378: instruction: find exact & approximate solutions to the problem.
106. One on One. Find two positive real numbers that differ by 1 and have a product of 1.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Find two positive real numbers..X AND Y SAY that differ by 1 and have a product of 1.
X-Y=1..................................I
XY=1
(X+Y)^2=(X-Y)^2+4XY=1^2+4*1=5
X+Y=SQRT(5).................................II
EQN.I+EQN.II GIVES
2X=1+SQRT(5)
X=(1+SQRT(5))/2=(2.236+1)/2=1.618
EQN.II-EQN.I..GIVES
2Y=SQRT(5)-1
Y=(SQRT(5)-1)/2=(2.236-1)/2=0.618
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