1. here goes......

2<sup>2x</sup> - 9 (2<sup>x</sup>) + 8 = 0

there are two answers for x: 3 and 0....but how to get them?

thx....  2.

3. Let u = 2<sup>x</sup>.

Then, 2<sup>2x</sup> - 9 (2<sup>x</sup>) + 8 = = u<sup>2</sup> - 9u + 8 = 0.

Factor: u<sup>2</sup> - 9u + 8 = (u - 8 )*(u - 1) = 0.

u = 8 or 1.

So, 2<sup>x</sup> = 8, or x = 3.

And, 2<sup>x</sup> = 1, or x = 0.  4. omg...why didn't i think of that??? thanks very much for helping.... geez...i need to brush up my maths...  5. No problem.

A lot of math is just recognizing patterns.  6. here's another math question....

it is given that -2 < m <= 4 and 3 <= n < 9 ........m and n are integers the maximum value of n / m is 8.......how? thx...  7. Originally Posted by randytsx
here's another math question....

it is given that -2 < m <= 4 and 3 <= n < 9 ........m and n are integers the maximum value of n / m is 8.......how? thx...
Thats ones easy. In this case its easier just to work out the 30 possible integers and compare (8 falls out quite quickly).

For general problems you have to compare some cases

1. The gcd(n, m) = 1 (else we can reduce the fraction to a smaller one)
2. Find the largest positive integer in the list (in our case 8) and divide it by the smallest positive integer on the list (in our case 1) such that condition 1 holds.
3. Find the smallest negative integer on the list (in our case -2) and divide it by the largest negative integer (in our case -1) so that condition 1. holds.

Compare the two answers you get -> 8 and 2, and from this we find the max of 8.  8. Oops = the gcd stuff is not needed, please ignore it  9. thx!!...but i'm wondering...

if ... -2 < m <= 4 and 3 <= n < 9...

and the largest postive integer on the list is 8 when
n < 9

....then why when

m > -2

the smallest negative integer is -2? sorry...i'm kinda weak at maths...and often get confused easily....  10. Originally Posted by randytsx
thx!!...but i'm wondering...

if ... -2 < m <= 4 and 3 <= n < 9...

and the largest postive integer on the list is 8 when
n < 9

....then why when

m > -2

the smallest negative integer is -2? sorry...i'm kinda weak at maths...and often get confused easily....
Oops another mistake (i shouldnt reply so late at night), the smallest negative integer is -1. I misread it as m >= -2  11. :? oh, thx...so how to find the values of n and m?.....or..the values of n and m may be different and not fixed?

sorry if this is a dumb question....but i'm really not good in linear inequalities...thx  12. [quote="randytsx"]:? oh, thx...so how to find the values of n and m?.....or..the values of n and m may be different and not fixed?

sorry if this is a dumb question....but i'm really not good in linear inequalities...thx[/quote
n and m depend on the problem at hand. But for these cases you just ask yourselves the questions 2 & 3 and compare the answers.  13. yes but with these...

it is given that

-2 < m <= 4
3 <= n < 9

m and n are integers

maximum value of n / m = 8

1. Find -> largest positive integer in the list (in our case 8) -> divide -> smallest positive integer (in our case 1).

2. Find -> smallest negative integer in the list (in our case -1) and divide it by the largest negative integer (in our case -1).
the two values obtained here are 8 and 1....

so I can find out the maximum value of n / m, which is a division...but how to find just the values of n and m?  Bookmarks
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