How good is your Mathematics?

[akv89]

I don't quite remember what happened to the last thread so here's a shiny new one.
Question: If x*y = 2 and x^2 + y^2 = 5, then x/y + y/x = ?

[Brown, Jon Brow]

2.5 ??

[J4MIE]

z :D

[Rollo]

2.5 ??

Confirmed!

xy=2
X^2+y^2=5

x=2/y

Sub for x:

(2/y)^2+y^2=5
4/Y^2+y^2=5
y=2

Sub for y:
2x=2
x=1

Sub for x & y:
1/2+2/1=2.5

Brown, Jon Brow wins :D

[tinchote]

Confirmed!

xy=2
X^2+y^2=5

x=2/y

Sub for x:

(2/y)^2+y^2=5
4/Y^2+y^2=5
y=2

Sub for y:
2x=2
x=1

Sub for x & y:
1/2+2/1=2.5

Brown, Jon Brow wins :D


It can be done in a slightly simpler way:

x/y + y/x = (x^2 + y^2) / (xy) = 5 / 2

This way you don't find x and y, but that was not part of the question :)

[billiaml]

So Brown, Jon Brow gets to try to stump us now?

[Rollo]

It can be done in a slightly simpler way:
x/y + y/x = (x^2 + y^2) / (xy) = 5 / 2
This way you don't find x and y, but that was not part of the question :)

I like this. This is quite an elegant solution to the problem. :D

[ioan]

It can be done in a slightly simpler way:

x/y + y/x = (x^2 + y^2) / (xy) = 5 / 2

This way you don't find x and y, but that was not part of the question :)

You get an A+! ;)

[Erki]

Maths is evil. :evil:

[tinchote]

Maths is evil. :evil:

Well, that's hard for me to say when it has been paying the bills for a couple decades now :D

[Erki]

But bills... what are bills at all? Aren't bills after all sums? Bills = Maths. Bills are evil => maths is evil. :evil:

[tinchote]

But bills... what are bills at all? Aren't bills after all sums? Bills = Maths. Bills are evil => maths is evil. :evil:

That's an interesting logic :D

[Brown, Jon Brow]

If only the questions in my Maths A-Level exams were as easy as that one ;)

:uhoh:

OK here we go. This question is from the January 2006 OCT Maths Core 3 exam paper :D

Solve, for 0 < θ < 360 degrees, the equation sec^2 θ = 4 tan θ - 2

(note that 'θ' = theta, not 8 (eight) ;) )

[tinchote]

My little girls - as usual - have stolen all my pens, so I had to this without writing, and I'm not that trustable. I seem to find two solutions, and those are when the tangent is either 1 or 3. The case 1 corresponding to θ = pi/4, and the other one would be arctan(3), whatever that is.

[donKey jote]

But that's not maths... it's flipping trigonometry :p :

[tinchote]

But that's not maths... it's flipping trigonometry :p :


That would probably merit a thread on its own: what is math? :D

[Alfa Fan]

A = Theta

tanA = 1 or 3 , A = 45,315,71.57,288.43 :)

Now differentiate

ln (4x+2)/7x

[Brown, Jon Brow]

The answer I have written down is

tan A= 1 0r 3

Therefore A = 45 or 71 or 225 or 251