What positive number is the square root of half itself?
Does this generalise?
We are not talking whole numbers here, eh?
Daniel
That's right. It doesn't have to be an integer.
0.5
Yes!
Could you give an explanation Jan? Obviously I could but yours might be better.
I translated the written statement to algebra as
x = √ (x/2)
then worked it through from there
x2 = x/2
2 x2 = x
2 = x / (x2)
2 = 1/x
x = 1/2
x = 0.5
It may be a bit long winded, but I always have to plod through without many shortcuts.
Thanks Jan, that's a clear way to think of it.
The only thing I would add is that 0 seems to fit the bill, if you try it, but it's ruled out because we are told the number is positive, i.e. > 0.
Square root is power 1/2, so we have
1/2 = (1/2 of 1/2)1/2
which seems quite neat!
We also have
1/3 = (1/3 of 1/3 of 1/3)1/3
and so on.
This could be why I'm registered to do MST124 from October. I don't know all the possible little maths wrinkles yet
Jan
Comments
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Does this generalise?
New comment
We are not talking whole numbers here, eh?
Daniel
New comment
That's right. It doesn't have to be an integer.
New comment
0.5
New comment
Yes!
Could you give an explanation Jan? Obviously I could but yours might be better.
New comment
I translated the written statement to algebra as
x = √ (x/2)
then worked it through from there
x2 = x/2
2 x2 = x
2 = x / (x2)
2 = 1/x
x = 1/2
x = 0.5
It may be a bit long winded, but I always have to plod through without many shortcuts.
New comment
Thanks Jan, that's a clear way to think of it.
The only thing I would add is that 0 seems to fit the bill, if you try it, but it's ruled out because we are told the number is positive, i.e. > 0.
Square root is power 1/2, so we have
1/2 = (1/2 of 1/2)1/2
which seems quite neat!
We also have
1/3 = (1/3 of 1/3 of 1/3)1/3
and so on.
New comment
This could be why I'm registered to do MST124 from October. I don't know all the possible little maths wrinkles yet
Jan