# Anyone know some basic maths, I need help :-D

#### krazykaj

##### Board Regular
Hi,

I've been asked to solve this:

Find the value of x and y if:
11 - 2√30 = x - y√30

I just can't seem to get it right/prove it .
Maybe I need to sleep on it and come back to it later . . .

However if anyone could give a hand/some assistance, I would be extremely grateful.
Even a hint in the right direction as a kick-start would be great . . . . :wink:

Thankyou kindly for you time.
Cheers
KJ

### Excel Facts

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11-2√30=x-y√30
11-2√30
=--------- = x-y
√30
11-60
=------- = x-y (multiplied by √30/√30)
30
=-1.63(recurring 3)=x-y
=y-1.63=x
=y=x+1.63

I get:

y=(x*v30-11*v30+2)/30

Hope that helps!

You can't possibly work out x and y (two variables). You'd need one to work out the other.

Here is the whole question, word for word:

Simplify by rationalising the denominator of:

√6 - √5
√6 + √5

Hence find the values of x and y if:

√6 - √5 = x - y√30
√6 + √5

√6 - √5 = 11 - 2√30
√6 + √5

(Which I hope is correct)

Thanks for all the posts so far, it'll give me something to work with :D
Cheers
KJ
(NOTE: Context of me asking the question: I'm just a student who studies at home via correspondence ('home school'), so I like to ask guys like you :D for initial help/explanations before I need to resort to contacting a ‘teacher’, explaining everything etc. (which can take a couple of days at least). Plus I’m also 100% certain, that most of you here know more than some of the teachers I get put into contact with
This question was just part of a quick ‘End-of-Topic’ questionnaire . . . And it’s the only one I couldn’t seem to fully get . . . well not to my satisfaction anyway)

Haven't you already worked it out?

Unless I'm misunderstanding something, x = 11 and y =2.

Andrew

Hi again,

Sorry to probably be so dense, however I'm now (I think) more confused than before with trying to work this out and fully understand it . . .

I have received the following as answers (some from other people elsewere)

First solution:
11 - 2 √30 = x - y√30
=
y = -[(11 - 2√30 - x) ÷ (√30)]

when x = 11
y = -[(11 - 2√30 - 11) ÷ (√30)]
y = -[(-2√30) ÷ (√30)]
y = -2

when x = -11
y = -[(11 - 2√30+ 11) ÷ (√30)]
y = -[(-2√30) ÷ (√30)]
y = 2

Second solution:
11 - 2√30 = x - y√30
=
(y - 2√30) = x - 11
or
√30 = (x - 11) ÷ (y - 2)

Third solution:
11 - 2√30 = x - y√30
=
11 - 2√30 = x - y
√30

11 - 60 = x - y (multiplied by √30 ÷ √30)
30

-1.6333 = x - y
y - 1.6333 = x
y = x + 1.6333

Fourth solution:
11 - 2√30 = x - y√30
=
y = (x√30 -11√30 + 2) ÷ 30

Fifth solution:
11 - 2√30 = x - y√30
=
x = 11 and y = 2

Aaaarrrgghhh
???????????????????

Given you have 2 unknown variables, you can mangle the formula any which way you like but AFAIK you can't solve it without substituting one of the unknown variables for a value.

The √5, √6 & √30 are all known values - to 4dp (not enough I know) they are 2.2361, 2.4495 & 5.4772 respectively. If you substitute these values into the formula, you end up with (excuse the formatting) :

2.4495 - 2.2361 = x - 5.4772y
2.4495 + 2.2361

this further breaks down to :

0.0455 = x - 5.4772y

which can be rearranged, this way :

x = .0455 + 5.4772y

or this way :

y = (x - .0455) / 5.477

which can also be represented as :

y = (x / 5.477) - 0.0083

Assuming x is a positive integer, then y can be any value starting from 0.174 (assuming x = 1).

Assuming y is a positive integer, then x can be any value starting from 5.523 (assuming y = 1).

Assuming both are positive integers then x = 11 and y = 2.

Andrew

krazykaj said:
Hi again,

Sorry to probably be so dense, however I'm now (I think) more confused than before with trying to work this out and fully understand it . . .

I have received the following as answers (some from other people elsewere)

First solution:
11 - 2 √30 = x - y√30
=
y = -[(11 - 2√30 - x) ÷ (√30)]

when x = 11
y = -[(11 - 2√30 - 11) ÷ (√30)]
y = -[(-2√30) ÷ (√30)]
y = -2

Incorrect. y = -(-2) = 2 when x = 11

when x = -11
y = -[(11 - 2√30+ 11) ÷ (√30)]
y = -[(-2√30) ÷ (√30)]
y = 2

Also incorrect. What happened to your 11's? They wouldn't cancel out here.

Second solution:
11 - 2√30 = x - y√30
=
(y - 2√30) = x - 11
or
√30 = (x - 11) ÷ (y - 2)

Incorrect. What happened to the sqrt 30 with the y?

Third solution:
11 - 2√30 = x - y√30
=
11 - 2√30 = x - y
√30

11 - 60 = x - y (multiplied by √30 ÷ √30)
30

-1.6333 = x - y
y - 1.6333 = x
y = x + 1.6333

Incorrect. You'd have to multiply everything by sqrt 30, not just the 2sqrt(30)

Fourth solution:
11 - 2√30 = x - y√30
=
y = (x√30 -11√30 + 2) ÷ 30

There is nothing wrong with the logic here, but does this help you?

Fifth solution:
11 - 2√30 = x - y√30
=
x = 11 and y = 2

Correct. Can you tell by looking at it? You have a number by itself (11) and a number in front of the sqrt(30) (2). X is the number by itself, so it must represent the 11. Y is in front of the sqrt(30), so it must represent 2.

Aaaarrrgghhh
???????????????????

Oaktree said:
Fourth solution:
11 - 2√30 = x - y√30
=
y = (x√30 -11√30 + 2) ÷ 30

There is nothing wrong with the logic here, but does this help you?

Yup. Because that's as far as you're going to get. There are an infinite number of solutions, since no values for x or y were specified in the question. It's a graph of a line.

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