Ratio equals

Question

Solve, what ratio with two integers is equal to the ratio  1 + \sqrt{5}  to  2 ?

I am getting 4:3 using conjugates, the actual question says 'nearly equal' and estimates that 8:5 is correct, but I believe that 4:3 is more accurate.

IanStewart · Answer

The ratio is not exactly equal to any ratio involving integers, which is why the question asks for an approximation. Since root(5) is greater than root(4), or 2, then 1 + root(5) must be greater than 3, and the ratio in question should be slightly greater than 3 to 2. Since 4 to 3 is less than 3 to 2, it should not be the right answer.

I3igDmsu · Answer

What answer are you getting if you use conjugates?

IanStewart · Answer

There's no reason to use conjugates here, but if you did, you'd find:

root(5) + 1 to 2
=   *   to 2* 
= 5 - 1 to 2*root(5) - 2
= 2 to root(5) - 1

It's harder to get an estimate now than it was in the original question, which is why it doesn't make much sense to use conjugates here. Still, even with a rough estimate of root(5) here, you can see that the answer should be somewhere between 3 to 2 and 2 to 1.

benpack03 · Answer

How about 13 to 8

root 5 aproximately equals 2.24, so 3.25 to 2 equals 13 to 8.......

rashminet84 · Answer

\sqrt{5} is almost equal to 2.2, 
so 3.2 : 2 (multiply by 5 to get integers on both sides)
you get 16 : 10
or 8 : 5

maliyeci · Answer

As integers increase, one can find a so near ratio. root 5 is something near 2,23. So equation comes near 1,62. One can say this 81/50. That is to say, something missing in question.

parimal · Answer

I got 13/8 as well. took underroot of 5 and added 1 and then divided by 2 =325/200 = 13/8

Ratio equals

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