Help Please (2 Viewers)

[Trenna N]

Hi,

My question is this:

Complete the table, such that the values of a and b satify the following equation: 1/a + 1/b = 1/8. The first solution has been given as 1/16 + 1/16 = 1/8. Need to find other 4 other solutions the top number must be a 1.

Thanks I am really stuck.

Trenna

 

[dodgyv]

a=16 b =16?????????????????????? thats some fcked up question soz cant help you there

 

[lyounamu]

Hi,

My question is this:

Complete the table, such that the values of a and b satify the following equation: 1/a + 1/b = 1/8. The first solution has been given as 1/16 + 1/16 = 1/8. Need to find other 4 other solutions the top number must be a 1.

Thanks I am really stuck.

Trenna

When a = 1, b=-8/7
When a = 2, b=-8/3
When a= 3, b= -24/5
When a = 4, b= -8

 

[Trenna N]

I know, its really hard. I probably didnt explain it too well. I need to find 2 demoninators as the numerators have to be the number 1. The question needs to add up to 1/8.

The lecturers example was 1/16 + 1/16 = 1/8. The question is 1/a + 1/b + 1/8. I need to do four more examples. I also need to do these questions for 1/a + 1/b = 1/6. Her example is 1/12 + 1/12 = 1/6. Its really hard, but thanks for helping.

Trenna

 

[tommykins]

There are an infinite number of solutions. Unless it states a,b > 0.

To make it easy, do a = 0 (if you're allowed), 1,2,3,4,5,6,7,8 etc. and use the calculator or solve it algebraically.

 

[dodgyv]

did u say this was a general maths question ><""" omg a 3unit student who cant do a general maths question 1/a crap lOl dammm....

 

[Trenna N]

Hi,

I am not doing maths at uni, I am majoring in history and english. A friend of mine emailed me her question to see if I could help. Unfortunately I havent done maths since high school which was 1985 so that is why I posted the question here.


Trenna

 

[tommykins]

Hi,

I am not doing maths at uni, I am majoring in history and english. A friend of mine emailed me her question to see if I could help. Unfortunately I havent done maths since high school which was 1985 so that is why I posted the question here.


Trenna

You see,

1/a + 1/b = 1/8

a+b/ab = 1/8

ab/a+b = 8

Thus, ab = 8a+8b. There is an infinite amount of solutions, unless the question is asking for a general formula to find out these solutions, there is more than 5 values for a and b.

 

[Iruka]

Egyptian fractions!!!


OK,
1/a + 1/b = 1/8

Multiplying through by 8ab, we have
8b+8a = ab

So ab - 8a -8b = 0.

Now we can add 64 to both sides of the equation, then we have

ab - 8a -8b + 64= 64,

which we can factor as

(a-8)(b-8) = 64.

Now I am assuming that you are looking for a and b that are positive whole numbers, which makes the solution quite simple.

The factors of 64 are 1, 2, 4, 8, 16, 32, and 64.

So one possibility is a-8 = 1 and b-8 = 64, i.e, a=9, b=72.

Go through the other pairs of factors and you will get the other solutions.

 

[PC]

1/a + 1/b = 1/8
b/ab + a/ab = 1/8
(a + b)/ab = 1/8
Now cross multiply:
8(a + b) = ab
8a + 8b = ab
8a = ab – 8b
8a = b(a – 8)
.: b = 8a/(a – 8)

So there's an equation for b in terms of a. You can substitute any value in for a and get a value for b.

If a = 1, b = 8(1)/(1 – 8) = 8/-7 = -8/7
If a = 2, b = 8(2)/(2 – 8) = 16/-6 = -8/3, etc.

If you want positive integral values of a and b then Iruka's method is pretty good. Alternatively we need a > 8 and a – 8 must also be a factor of either a or 8.

If a = 9, b = 8(9)/(9 – 8) = 72/1 = 72
If a = 10, b = 8(10)/(10 – 8) = 80/2 = 40
If a = 12, b = 8(12)/(12 – 8) = 96/4 = 24
If a = 16, b = 8(16)/(16 – 8) = 128/8 = 16
If a = 24, b = 8(24)/(24 – 8) = 192/16 = 12
If a = 40, b = 8(40)/(40 – 8) = 320/32 = 10
If a = 72, b = 8(72)/(72 – 8) = 576/64 = 9

That's it.