Melody

In year 12 which is about 17 years of age usually.

Thanks guest, could you explain your answer please 

what exactly is the question asking....

Let 'a' and 'b' be positive integers such that

\(\frac{a^2 + b^2}{ab+1}=c \qquad where \quad c\in Z\)

Show that 

\(\frac{a^2+b^2}{ab+1}=k^2 \qquad where\quad k\in Z\)

in other words show that c is a square number.

Ok now I understand the question. But I would like you to elaborate on your answer :)

Thank you.

What does it take to score a 7 in HL Maths in the IB Curriculum?

This is a international forum.

Most of us have no idea what you are talking about!

Very nicely answered Hectictar :)

You forgot that 3x>y

Here is the system of equations

Can you understand what i have done to determine the maximum profit?

I liked it :))

It is the corner of a square, or the pointy bit on an angle, or the turning point on a curve.  :)

Yes, I think it makes sense too :)

Maths has a level of difficulty for everyone.  

So if you are stupid so is everyone else :)

Maybe it should just be simplify????

 tan x cos 2x + tan x + sin 2 x

\(tan x *cos 2x + tan x + sin 2 x\\ =\frac{sinx}{cosx} *(cos^2x-sin^2x)+ \frac{sinx}{cosx} + 2sinxcosx\\ =sinxcosx-\frac{sin^3x}{cosx}+ \frac{sinx}{cosx} + 2sinxcosx\\ =3sinxcosx-\frac{sin^3x}{cosx}+ \frac{sinx}{cosx} \\ =3sinxcosx- \frac{sinx}{cosx} (sin^2x-1)\\ =3sinxcosx- \frac{sinx}{cosx} (-cos^2x)\\ =3sinxcosx+ (sinxcosx)\\ =4sinxcosx\\ =2sin2x \)

Lets see if I could have done this more simply....

\( tan x cos 2x + tan x + sin 2 x\\ = tan x (cos^2x-sin^2x) + tan x + sin 2 x\\ = tan x (cos^2x-sin^2x+1) + sin 2 x\\ = tan x (cos^2x+cos^2x) + sin 2 x\\ =\frac{sinx}{cosx} (2cos^2x) + sin 2 x\\ =2sinxcosx + sin 2 x\\ =sin2x + sin 2 x\\ =2sin2x \\\)

So it can be seen that 

tan x cos 2x + tan x = sin 2 x

which I guess was meant to be the question in the first place.   (as hectictar and CPhill have already noted.  Thanks guys. :)