Extension Maths Query (1 Viewer)

[Finx]

2. i) Show that 1/(p^2+pq) + 1/(q^2+pq) = 1/pq

I figured this one out, but for the next bit:

ii) Hence express 1/5 in the form 1/a + 1/b for some positive integers a and b.

What the hell does this mean? >_<

 

[bored of sc]

Maybe:
Let p = 1 and q = 5.

Substitute it the equation of part (i)
= 1/(1² + 1x5) + 1/(5² + 1x5)
= 1/6 + 1/30

Therefore a = 6 and b = 30.

Hmm...

 

[shaon0]

2. i) Show that 1/(p^2+pq) + 1/(q^2+pq) = 1/pq

I figured this one out, but for the next bit:

ii) Hence express 1/5 in the form 1/a + 1/b for some positive integers a and b.

What the hell does this mean? >_<

LHS=1/(p^2+pq) + 1/(q^2+pq)
=q^2+2pq+p^2/(q^2+pq)(p^2+pq)
=(p+q)^2/q(p+q)*p(p+q)
=(p+q)^2/pq(p+q)
=(p+q)/pq...
What is your solution for the first part?

ii) Let a=p(p+q), b=q(p+q), pq=5
Sub a value into b value.
b-q^2=a-p^2
(p-q)(p+q)=a-b
p+q=(a-b)/(p-q)

 

[lyounamu]

2. i) Show that 1/(p^2+pq) + 1/(q^2+pq) = 1/pq

I figured this one out, but for the next bit:

ii) Hence express 1/5 in the form 1/a + 1/b for some positive integers a and b.

What the hell does this mean? >_<

1/(p^2+pq) + 1/(q^2+pq) = 1/pq

1/5 = 1/(5 x 1)
= 1/(5^2 + 5 x 1) + 1/(1^2 + 5 x 1) = 1/30 + 1/6

Therefore, a = 30 and b=6 as bored of sc said.

 

[Finx]

LHS=1/(p^2+pq) + 1/(q^2+pq)
=q^2+2pq+p^2/(q^2+pq)(p^2+pq)
=(p+q)^2/q(p+q)*p(p+q)
=(p+q)^2/pq(p+q)
=(p+q)/pq...
What is your solution for the first part?

LHS:
= 1/p(p+q) + 1/q(p+q)
After multiplying by q/q and p/p respectively
= q/pq(p+q) + p/pq(p+q)
= (p+q)/pq(p+q)
= 1/(p+q)

1/(p^2+pq) + 1/(q^2+pq) = 1/pq

1/5 = 1/(5 x 1)
= 1/(5^2 + 5 x 1) + 1/(1^2 + 5 x 1) = 1/30 + 1/6

Therefore, a = 30 and b=6 as bored of sc said.

Ah I see, p=5 and q=1 (for the positive factors of 5), then after subbing etc you get the 1/30 and 1/6. Sweet, thanks =D

 

[shaon0]

LHS:
= 1/p(p+q) + 1/q(p+q)
After multiplying by q/q and p/p respectively
= q/pq(p+q) + p/pq(p+q)
= (p+q)/pq(p+q)
= 1/(p+q)



Ah I see, p=5 and q=1 (for the positive factors of 5), then after subbing etc you get the 1/30 and 1/6. Sweet, thanks =D

Oh...okay

 

[Finx]

Er, whoops, the last line there should be 1/pq

My bad ._.