SOLUTION: Checking my math on this one, we're working on Quadratics this week: Find two positive real numbers that differ by 1 and have a product of 1

Algebra.Com
Question 48192: Checking my math on this one, we're working on Quadratics this week:

Find two positive real numbers that differ by 1 and have a product of 1

Answer by atif.muhammad(135)   (Show Source): You can put this solution on YOUR website!
Find two positive real numbers that differ by 1 and have a product of 1


Let one of the real number be x and the other be y.

Both differ by 1: y-x = 1

Both have a product of 1 : xy = 1

We have a pair of simultaneous equations

y-x = 1....(1)
xy = 1....(2)

Manipulate (1):

y-x = 1

y = (x+1)....(3)

Substitute (3) into (2):

xy = 1

x(x+1) = 1

x^2 + x = 1

x^2 + x -1 = 0  ---- Oooo...a quadratic equation!

I'm not going to bother factorising it as I remember the answer to this equation. It gives a golden ratio as its' answer -- something like 0.618.

So if x = something like 0.618

Then y = x + 1 = something like 1.618

Hope that helps!


RELATED QUESTIONS

Please help! I have no idea how to even approach this problem. Thank you. One on one.... (answered by venugopalramana)
instruction: find exact & approximate solutions to the problem. 106. One on One.... (answered by venugopalramana)
How in the world?? Again my book doesnt have an equation on how to solve this and... (answered by stanbon)
Find two positive real numbers that differ by 1 and have a product of 1. (answered by longjonsilver)
Find two positive real numbers that differ by 1 and the product of 1. (answered by kev82)
Find two positive real numbers that differ by 1 and have a product of... (answered by longjonsilver)
Find two positive real numbers that differ by 1 and have a product of... (answered by stanbon)
find two positive real numbers that differ by 1 and have a product of... (answered by ankor@dixie-net.com)
Find two positive real numbers that differ by 1 and have a product of... (answered by ankor@dixie-net.com)