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....

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....
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.
omg...why didn't i think of that???
thanks very much for helping....
geez...i need to brush up my maths...
No problem.
A lot of math is just recognizing patterns.
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).Originally Posted by randytsx
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.
Oops = the gcd stuff is not needed, please ignore it
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
instead of 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 >= 2Originally Posted by 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="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.
yes but with these...
the two values obtained here are 8 and 1....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).
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?
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