Both are correct - test with a = 4 and a=9Is 1 or 2 correct? View attachment 32277
But what if it was 4/2Both.
"What" was 4/2? Use a calculator and check!But what if it was 4/2
If it was 4/2 instead of 3/2, you would just have a 4 where you now have a 3.But what if it was 4/2
No no! That test is not valid as it doesn't confirm the results for all real numbers. You know this. You are extremely good in math (much better than me!) but you are still a trained engineer and make silly mathematical comments like you just did!Both are correct - test with a = 4 and a=9
Testing is not the same as proving.No no! That test is not valid as it doesn't confirm the results for all real numbers. You know this. You are extremely good in math (much better than me!) but you are still a trained engineer and make silly comments like you just did!
Yes, SK did say to test with a=4 and a=9 but he clearly meant that will serve as a proof for all numbers.Testing is not the same as proving.
Oh dear me. I'm not liking this!You are correct to be concerned with fractional exponents.
For example in x^(2/4) it allows x to be negative. The reason is if x<0, then x^2>0 and you can now compute (x^2)^(1/4).
Now if you reduce 2/4 to 1/2 you have trouble as x^(1/2) does not allow x<0. Be careful!
No I don't think he meant that.Yes, SK did say to test with a=4 and a=9 but he clearly meant that will serve as a proof for all numbers.
This troubled me too since I thought that you could ALWAYS replace equals with equals but apparently that isn't true.Oh dear me. I'm not liking this!
So you are saying that x^(2/4) is not equal to x^(1/2) ??
Therefore they are not equal to one another. They have different domains!I agree that in \(\displaystyle \sqrt[4]{a^2}\), \(\displaystyle a\) can be negative, but not in \(\displaystyle \sqrt{a}\).
Yes I agree -when using radical notation. Not sure when using exponent notation though as in post #12.Therefore they are not equal to one another. They have different domains!
I am sure that a^(1/2) does not equal a^(2/4).Yes I agree -when using radical notation. Not sure when using exponent notation though as in post #12.
Have you had your coffee this morning?I am sure that a^(1/2) does not equal a^(2/4).
Steven,Yes, SK did say to test with a=4 and a=9 but he clearly meant that will serve as a proof for all numbers.