maths question

[Fat Tone]

p + q = 10

p * q = 18

what is p^2 + q^2?

[degrub]

solve for q in the first two eqn. set them equal to each other and get an expression only in terms of p
arrange it in the canonical form ax^2 + bx + c =0

use the quadratic equation solution for canonical form

x= (-b+sqrt(b^2-4ac ))/2a

and

x= (-b-sqrt(b^2-4ac ))/2a

then solve for q in the original equations for each P
then calculate P^2 + Q^2 for each of the sets of Ps and Qs

[UtwigMU]

p = 5 + sqrt 7
q = 5 - sqrt 7

p^2 + q^2 = 64

[degrub]

correct final answer. The P&Qs have complementary answers. Squaring each makes it not matter for the final result. They are one of those odd symmetries.

[Brian Ellis]

Just watch your p's and q's!

[Fat Tone]

Many thanks, It's beeen a long time since I did that stuff in anger.

It is part of my son's maths homework. There's a large paper to do and he can do most of the rest with his eyes shut. This one is on a different level and I think could be a typo as they are usually simple factors.

Cheers!

T.

[cjolley]

How old is he?
We run across clinkers like that in my daughter's homework every once in a while too.
Last week it was a geology crossword where one of the words was simply not in the book.
She's 12 now

[Umfriend]

p = 5 + sqrt 7
q = 5 - sqrt 7

p^2 + q^2 = 64

correct final answer. The P&Qs have complementary answers. Squaring each makes it not matter for the final result. They are one of those odd symmetries.

Strictly speaking it is not the correct answer as p equals 5 +/- sqrt 7 and q equals 5 -/+ sqrt 7 where the signs are conditional on each other (one must be positive and the other negative).

[VJ]

Umf: p and q were never asked...

And it is a simple product if you consider it this way:
(p+q)^2 = p^2 +2pq + q^2
which means
p^2 + q^2
= (p+q)^2 -2pq
= 100-2*18=64

[Umfriend]

Ah, you are right, silly me.

[Fat Tone]

Beautiful, VJ! Reminds me why I loved maths when I had a brain

Thanks all.

Luke has just started his GCSEs, will take them in summer 2014.

[cjolley]

Luke has just started his GCSEs, will take them in summer 2014.

Which, to someone in the US, means he is somewhere between 0 and 100 yo

[Umfriend]

OK, here is a joke I _do_ not get.

[Fat Tone]

That's right Chuck, how did you guess?

He's about to turn 15 and is in year 10. GCSEs are taken in year 11, A-levels in year 13 and then they go to University for 3+ years.

When I were a lad GCSEs were called O-levels and were assessed by exam at the end. Things are now returning to that and continual assessment is being scaled back.

[VJ]

Beautiful, VJ! Reminds me why I loved maths when I had a brain

My highschool teacher really drilled us with those factors... and it still seems to have effects...

If you like maths, you'll love this one:
Imagine a rope that fits tightly around the equator. Now, imagine a second rope that "floats" 1m above the first one, everywhere. How much longer is that rope? And what if we do the same with a rope around a tennis ball? (the answer is quite counter intuitive)