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Comment on Conclusion Based on Root
3.5 is not integer it is real
That's correct. So, we can
That's correct. So, we can automatically rule out 3.5 as a possible solution.
One of the rule say if x>1
I thought of the same rule while encountering the question. But then I have a doubt why we took 0 as well?
You're correct to say that,
You're correct to say that, if x > 1, then √x < x, however this rule applies to x-values that are greater than 1.
When it comes to √0, the same rule does not apply.
Here, √0 = 0
Does that help?
Cheers,
Brent
As I go on solving the
I must be more careful about not ignoring the premise while solving.
I agree!
I agree!
I often miss seeing important words (like INTEGER, POSITIVE, or CONSECUTIVE), which totally throws off the solution.
Hi Brent,
1.4 and 1.7 are also not integers? Why are we selecting these then?
Thanks,
Ketan
We're not selecting 1.4 and 1
We're not selecting 1.4 and 1.7 as possible values of x.
We're selecting 2 and 3 as possible values of x.
We're told that √x < 2
If x = 2, then √2 ≈ 1.4
Since 1.4 < 2, we know that x = 2 is a solution to the inequality √x < 2
Likewise, since √3 ≈ 1.7, and since 1.7 < 2, we know that x = 3 is another solution to the inequality √x < 2
Does that help?
Cheers,
Brent
Tricky! 3.5 is not an
That's right. Some of the
That's right. Some of the most common/crucial words that students often miss include:
- POSITIVE
- NEGATIVE
- INTEGER
- NON-NEGATIVE
- DIFFERENT (as in "x, y, and z are DIFFERENT positive integers")