Get into ax²+bx+c=0 form
subsitute u=x⁴
x⁸-3x⁴+2=0
(x⁴)²-3(x⁴)+2=0
u²-3u+2=0
factor
(u-2)(u-1)=0
set to zero
u-2=0
u=2
u-1=0
u=1
wait, u=x⁴
2=x⁴
![\sqrt[4]{2}=x](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B2%7D%3Dx)
1=x⁴
+/-1=x
the subsitution is u=x⁴
and the possible values for x are -1,
, and 1
A
rational number is any number that can be written as the
ratio between two other numbers i.e. in the form
Part A:
An easy choice that makes sense is 7.8, right in the middle. To prove that it's rational we need to write it as a ratio. In this case we have
Part B:
We need a number that can't be written as a ratio (because it neither terminates nor repeats). Some common ones are
,
,
and
so it makes sense to try and use those to build our number. In this case
works nicely.
Answer: $51
60 * .15 = 9
60 - 9 = $51
Not sure is this is right but if the chemist wants to make the solution 35% acidic then he can use all of the 30% acid and 5% of the 45% acid.
B, the first differences are not the same , that proves it is not linear. The second set of differences are the same this shows it is a quadratic function.
