[ASK] Exponents and Roots

Monox D. I-Fly · 2019-02-26 21:14:43

The result of

for x = 4 and y = 27 is ....
a.
b.
c.
d.
e.

I got stuck at

and don't know how to continue to reach one of the options. By the way, don't you think that 7 is suspicious?

Bob · 2019-02-27 02:24:27

hi Monox D. I-Fly

I too got stuck with this. So I tried evaluating the expression and the five possible answers and could find none that worked.

x^(5/6) seems to be a sticking point for me as that leads to a cube root of 2 not a square root. The answer must have a root of 3 in it.

If we're looking for a minimum typo to make this 'do-able' then losing the 7 would be a start … but that power 5/6 will have to change too … maybe 5/4 ???

I'll try exploring alternatives.

Bob

Grantingriver · 2019-02-27 04:15:09

You did not get the correct answer because non of them is, in fact, a correct answer!! This can be demonstrated by substitution as follows:

however we have

which is the required proof. Sorry but this is the true situation!!

Last edited by Grantingriver (2019-02-27 20:59:49)

phrontister · 2019-02-27 12:03:36

Hi Grantingriver,

I agree with what you said, but I tried Monox D. I-Fly's problem in my calculator, Excel and Mathematica and get approx -574.028.

My Mathematica formula is N[(7x-9/2Surd[y^5, 6])/((x^(5/6)-6y^(-1/3))x^-2)], and my calculator and Excel methods follow that line.

I can't think what I might have done wrong...

Last edited by phrontister (2019-02-27 14:58:20)

Monox D. I-Fly · 2019-02-27 13:50:54

According to you, what part of the question should be gotten rid of to reach one of the options?

Grantingriver · 2019-02-27 20:46:14

Hi phrontister, you are right I forgot to put the parentheses about the numerator when I performed the calculation (your answer is the correct one). Thank you to mention that (I have changed the number)

Last edited by Grantingriver (2019-02-27 21:00:35)

phrontister · 2019-02-28 00:44:12

Ah yes, of course.

I tried a few things in a brief attempt to work out how you got that answer, but didn't think of the missing parentheses.

Bob · 2019-02-28 06:12:44

I have decided to assume that there are several errors in this question. As the five possible answers are very similar it seems more likely that these lie in the start expression.

x^{5/6) leads to a cube root of 2 whereas we are hoping for a square root of 2. It is possible to show that no rational multiple of the first can give the second so that 6 must be in error. More likely a 4. This leads nicely to the (1+2root2) part of an answer.

56 is indeed a problem. How can a numerator with an integer and a root 3 lead to just a root 3. So I have altered the minus sign to a times sign.

9/2 leads to an 81 in the answer. Could it be 9^(1/2) rather than 9 times 1/2 ?

And x^-2 at the denominator leads to an answer that is far too large. Given that this is an exercise in fractional powers perhaps it should be x^(1/2)

So my suggestion is

This does lead to one of the given answers. You can have a try or uncover my hidden working.

Bob

Monox D. I-Fly · 2019-02-28 14:02:08

bob bundy wrote:

I have decided to assume that there are several errors in this question. As the five possible answers are very similar it seems more likely that these lie in the start expression.
x^{5/6) leads to a cube root of 2 whereas we are hoping for a square root of 2. It is possible to show that no rational multiple of the first can give the second so that 6 must be in error. More likely a 4. This leads nicely to the (1+2root2) part of an answer.
56 is indeed a problem. How can a numerator with an integer and a root 3 lead to just a root 3. So I have altered the minus sign to a times sign.
9/2 leads to an 81 in the answer. Could it be 9^(1/2) rather than 9 times 1/2 ?
And x^-2 at the denominator leads to an answer that is far too large. Given that this is an exercise in fractional powers perhaps it should be x^(1/2)
So my suggestion is
This does lead to one of the given answers. You can have a try or uncover my hidden working.

Bob

Aw, thank you Bob! You really are a genius!

Math Is Fun Forum

#1 2019-02-26 21:14:43

[ASK] Exponents and Roots

#2 2019-02-27 02:24:27

Re: [ASK] Exponents and Roots

#3 2019-02-27 04:15:09

Re: [ASK] Exponents and Roots

#4 2019-02-27 12:03:36

Re: [ASK] Exponents and Roots

#5 2019-02-27 13:50:54

Re: [ASK] Exponents and Roots

#6 2019-02-27 20:46:14

Re: [ASK] Exponents and Roots

#7 2019-02-28 00:44:12

Re: [ASK] Exponents and Roots

#8 2019-02-28 06:12:44

Re: [ASK] Exponents and Roots

#9 2019-02-28 14:02:08

Re: [ASK] Exponents and Roots

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