# Techniques For Solving Equations and Inequalities

• Jan 3rd 2011, 04:36 PM
abc10
Techniques For Solving Equations and Inequalities
Okay, so im facing a little difficulty with some of this, for example:

$\displaystyle 5secx=-x^2, 0<x<pi$

So you have to make LS=RS using trial and error. Now thats all find and dandy except that the answer is 2.5. For this, one side is positive the other is negative...
Another question is for the x must be between o and pi, does that mean I can only use numbers between 0 and 3.14 or is that some sort of radian measure?

$\displaystyle cosx=1/x, -4<x<0$

The answer is -2.1???? Wouldn't -1 make much more sense?

Im probably missing something simple here, but im going crazy nonetheless.
• Jan 3rd 2011, 05:18 PM
skeeter
Quote:

Originally Posted by abc10
Okay, so im facing a little difficulty with some of this, for example:

$\displaystyle 5secx=-x^2, 0<x<pi$

So you have to make LS=RS using trial and error. Now thats all find and dandy except that the answer is 2.5. For this, one side is positive the other is negative...
Another question is for the x must be between o and pi, does that mean I can only use numbers between 0 and 3.14 or is that some sort of radian measure?

$\displaystyle cosx=1/x, -4<x<0$

The answer is -2.1???? Wouldn't -1 make much more sense?

Im probably missing something simple here, but im going crazy nonetheless.

you'll have to solve these using technology (a calculator) ... there is no elementary method to do so by hand.

graph $\displaystyle y = 5\sec{x} + x^2$ and look for the zero(s) of y for x-values between 0 and $\displaystyle \pi$

same for the second ...

graph $\displaystyle \displaystyle y = \cos{x} - \frac{1}{x}$ and look for zero(s) in the given interval for x.