MHB Calculating M and the Unit Digit of M^2003

[anemone]

Let $$x$$ be a real number and let $$M=\frac{3x-1}{1+x}-\frac{\sqrt{\mid x\mid-2}+\sqrt{2-\mid x \mid}}{\mid 2-x \mid}$$.

Find $$M$$ and also the unit digit of $$M^{2003}$$.

 

[topsquark]

Let $$x$$ be a real number and let $$M=\frac{3x-1}{1+x}-\frac{\sqrt{\mid x\mid-2}+\sqrt{2-\mid x \mid}}{\mid 2-x \mid}$$.

Find $$M$$ and also the unit digit of $$M^{2003}$$.

Just a moment and I'll have it. I just have to program Excel...

-Dan

 

[kaliprasad]

Let $$x$$ be a real number and let $$M=\frac{3x-1}{1+x}-\frac{\sqrt{\mid x\mid-2}+\sqrt{2-\mid x \mid}}{\mid 2-x \mid}$$.

Find $$M$$ and also the unit digit of $$M^{2003}$$.

We are taking square root of |x| - 2 and its –ve so it has to be zero
So |x| - 2 = 0 or x = 2 or – 2
x cannot be 2 as |2-x| is in denominator
so x = - 2
hence putting the value x = -2 we get M = 7
as M^4 = 1 mod 10
M^2000 = 1 mod 10 or M^2003 = M^3 mod 10 = 343 mod 10 or 3
3 is the unit digit

 

[anemone]

We are taking square root of |x| - 2 and its –ve so it has to be zero
So |x| - 2 = 0 or x = 2 or – 2
x cannot be 2 as |2-x| is in denominator
so x = - 2
hence putting the value x = -2 we get M = 7
as M^4 = 1 mod 10
M^2000 = 1 mod 10 or M^2003 = M^3 mod 10 = 343 mod 10 or 3
3 is the unit digit

Hi kaliprasad,

Thanks for taking the time to participate in this challenge problem and I can tell how much you enjoyed working with some of the problems that I posted here and in case if you have any interesting mathematics problems to share with us, please feel free to do so! :p

Just a moment and I'll have it. I just have to program Excel...

-Dan

Hi Dan,

Thank you for the reply and you know what, you're one of the clever $$\cap$$ humorous member at MHB!