Melody

Yes thanks for posting clearly.   

Here is the version I would have liked best 

\(\text{The number }\;(\sqrt{2}+\sqrt{3})^3 \text{ can be written in the form }\\a\sqrt{2} + b\sqrt{3} + c\sqrt{6}, \text{ where $a$, $b$, and care integers. What is a+b+c ?}\)

I like this version best becasue it is the easiest to copy and to work on.     

The number (√2+√3)³ can be written in the form a√2+b√3+c√6, where a, b, and c are integers. What is a+b+c? 

\((\sqrt2+\sqrt3)^3=(\sqrt3)^3+3(\sqrt3)^2(\sqrt2)+3(\sqrt3)(\sqrt2)^2+(\sqrt2)^3\\ \)

Now expand it out and get the answer for yourself.  If you have new problems with this question then let us know.

Thanks Tertre, I figured that there must be but I am not good at remembering tricks. :/

prob of H,C,D then S   = 1/256

any order   4! = 24

24/256 = 3/32

OR

1*(3/4)*(1/2)*(1/4) = 3/32

Ok I did it 2 different ways and both times I got 3/32.  

Thanks Chris :)

f(x)=x^3

f(2)+f(-2)=2^3+(-2)^3 = 8+-8 = 0

I think questions like this one are always really hard to understand and I would like another mathematician to check my answer.

Use my pic, which is near enough to the same.

Think about a horizontal line through the graph.  

At the top it will pass through the graph twice so  g(c)=2

Here is a pic

I have drawn six horizonal lines.

For the top (purple - 1st ) one    f(x)=-2

this crosses the graph f(x) at 2 different x values so  g(-2)=2

the next horizontal line (black 2nd )  palsses through 4 points so  g(-2.8)=4

the 3rd horizontal line (red )  palsses through 6 points so  g(-3.4)=6

the 4th horizontal line (blue )  palsses through 5 points so  g(-4)=5

the 5th horizontal line (green)  palsses through 4 points so  g(-5)=4

the bottom horizontal line (purple )  palsses through 2 points so  g(-6.7)=2

So g(c) can be 2, 4, 5, or 6       

The average of the distict values of g(c) = (2+4+5+6)/4 = 17/4 = 4.25

I am pretty sure that is correct.

I would do it the same way as shown on this video.