Math problem- any experts here?

[newtohobby]

My son needs some help but I can't lol

supposedly you have to use some formula for this

1. what fraction is added to its reciprocal gives 2(1/6)
2. find 2 numbers whose difference is 7 and the difference of whose cubes is 1267
3. find 2 numbers whose difference is 10 and the sum of whose squares is 250

any help would be appreciated. Thanks

 

[EraserNips]

for number 1: not any good at fractions and reciprocals... sorry..

for number 2: x^3 - y^3 = 1267 and x = y + 7 so:

(y+7)^3 - y^3 = 1267

for number 3: x^2 + y^2 = 250 and x = y + 10 so:

(y+10)^2 + y^2 = 250

http://jdsmathnotes.com/demos/probs2.htm

hope this helps... I think I've set up the equations correctly..

 

[Mr. Lucky]

I hate math! Never liked it. (yes it's important to learn)


80% people are all geeks!

 

[blackrock13]

For the first one

Let n = the number
Then n + 1/n = 13/6

Now, we have to get rid of the n on the bottom of 1/n:

n(n + 1/n) = n(13/6)
n^2 + n = 13n/6

Now get rid of the 6 on the bottom of 13n/6:

6(n^2 + 6n) = 6(13n/6)
6n^2 + 6n = 13n

Set equal to 0:

6n^2 + 6n - 13n = 0

Simplify:

6n^2 - 7n = 0

n(6n - 7) = 0

This gives two solutions for n: 0 and 7/6. It can't be 0, so it has to be 7/6

I knew that. I posted that back in .......... wait, oh sorry.

Wrong thread. Pump pump.

 

[blackrock13]

I hate math! Never liked it. (yes it's important to learn)


80% people are all geeks!

Statistics is not one of your strengths. True?

 

[basketcase]

For the first one
...
This gives two solutions for n: 0 and 7/6. It can't be 0, so it has to be 7/6

7/6 + 6/7 = 55/42 not 13/6

The answer is 2/3 (or 3/2)

x/y + y/x = 13/6

(x^2 +y^2)/xy = 13/6

xy=6 factors are 6, 1 or 2, 3
6^2 + 1^2 = 37 - doesn't work

2^2 + 3^2 = 4 + 9 = 13

X=2, y+3

check 2/3 + 3/2 = 4/6 + 9/6 = 13/6 = 2 1/6



p.s. Be sure to have your son thank us

 

[Don]

Wow, TERB is now a place for students to get help for the Math homework! Amazing!

 

[blackrock13]

and 46% of statistics are made up

Reference please!

 

[Mia.Colpa]

7/6 + 6/7 = 55/42 not 13/6

Actually 7/6 + 6/7 = 85/42, not 55/42, regardless it's wrong as you said. Your methodolgy is correct and your answer is correct.

 

[ClassAct]

2. find 2 numbers whose difference is 7 and the difference of whose cubes is 1267:

a) x-y =7 => (x-y)^2=49 => <a1> x^2-2xy+y^2=49
b) x^3 -y^3 = 1267 => (x-y)(x^2+xy+y^3)=1267 => 7(x^2+xy+y^2)=1267 => <b1> x^2+xy+y^2 = 181

then <b1> - <a1> => 3xy=132 or xy=44

so you are left with, x-y = 7 and xy = 44.

Many ways to solve for xy, but the easiest is just trial and error. Two positive integers that multiply to 44 and whose difference is 7 are the numbers x= 11 and y=4.



3. find 2 numbers whose difference is 10 and the sum of whose squares is 250

a) x-y = 10 => (x-y)^2=100 => <a1> x^2-2xy+y^2 = 100
b) x^2 + y^2 = 250

(b) - <a1> => 2xy=150 => xy=75

So you are left with x-y=10 and xy=75, which upon trial an error, quickly yields you x=15 and y=5, assuming positive integers.

 

[civic82]

.....n(n + 1/n) = n(13/6)
n^2 + n = 13n/6.....

No math genius here but shouldn't n*1/n be "1" but not "n"?
Then the next line should be n^2+1=13n/6
6n^2+6=13n
6n^2-13n+6=0

basketcase: You are awesome!!!