mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} &\text{Find the number of integer values } \hspace{.33em}\\~\\ &\dfrac{15x^2+2x+1}{x^2-2x-1}\hspace{.33em}\\~\\ &\text{doesn't satisfy } \hspace{.33em}\\~\\ \end{align}}\)
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Hi math, Does that mean the number of integer values, which can not be written in the form:\[\dfrac{15x^2+2x+1}{x^2-2x-1}\]?
mathmath333
  • mathmath333
i mean the number of integer values the expression \(\dfrac{15x^2+2x+1}{x^2-2x-1}\) not take
anonymous
  • anonymous
aha that's right, so we just need to find the range of function

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More answers

anonymous
  • anonymous
\[y=\dfrac{15x^2+2x+1}{x^2-2x-1}\]find \(x\) in terms of \(y\), find the domain of inverse
anonymous
  • anonymous
@mukushla exact !
mathmath333
  • mathmath333
what u mean by x interms of y
anonymous
  • anonymous
solve the equation . and deal with y as a parameter
Ehsan18
  • Ehsan18
Separate x i.e. find x = ? and replace y with x afterwards.
mathmath333
  • mathmath333
u mean this http://www.wolframalpha.com/input/?i=solve+y%3D%5Cdfrac%7B15x%5E2%2B2x%2B1%7D%7Bx%5E2-2x-1%7D+for+x
ganeshie8
  • ganeshie8
Following mukushla's hint \[\large y=\dfrac{15x^2+2x+1}{x^2-2x-1}\] cross multiplying and rearranging gives \[\large (15-y)\color{red}{x^2}+(2+2y)\color{red}{x}+y+1 = 0\] This is a quadratic in \(\color{red}{x}\) you may use the discriminant to find the domain
mathmath333
  • mathmath333
ok, d=8(y+1)(y-7)
ganeshie8
  • ganeshie8
how?
mathmath333
  • mathmath333
from this -> (2+2y)^2-4(15-y)(y+1)
ganeshie8
  • ganeshie8
Ohk.. Notice that \(D \ge 0\) for the quadratic equation to make sense in real numbers
mathmath333
  • mathmath333
\(y>=7 ,y<=-1\)
ganeshie8
  • ganeshie8
those are the values the given rational expression ever takes
mathmath333
  • mathmath333
is infinite numbers answer
ganeshie8
  • ganeshie8
answer should be {0,1,2,3,4,5,6}
Ehsan18
  • Ehsan18
no but these numbers satisfy the equation
mathmath333
  • mathmath333
oh ok thnx
Ehsan18
  • Ehsan18
what on earth the question says does not satisfy??
ganeshie8
  • ganeshie8
|dw:1434277279587:dw|
anonymous
  • anonymous
The directions could be more clear. This might be better. "What integer values does the expression not attain. " or "What integer values does the function not attain. "

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