1/ x^2-10x - 8
I know I have to solve for zero and factor it but when I do it just comes out 1, -5 but the awnser is -1 ,5 ... I just dont understand why ? Sorry math is the subject I struggle with most .Thank you
It math course they teach you whenever they write a function they always assume all possible values that 'x' can take since you have a fraction,Originally Posted by starbrite
$\displaystyle \frac{1}{x^2-10x-8}$
It can be any value EXCEPT when the denominator is zero.
Thus,
$\displaystyle x^2-10x-8\not =0$
Since this is not factorable use quadradic formula,
$\displaystyle x=\frac{10\pm \sqrt{100+64}}{2\cdot 1}$
Simplfy,
$\displaystyle x=\frac{10\pm 2\sqrt{41}}{2}$
Thus,
$\displaystyle x=5\pm \sqrt{41}$
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To make things clearly, let me explain,
$\displaystyle \sqrt{100+64}=\sqrt{164}=\sqrt{4\cdot 41}=2\sqrt{41}$
And, in the final step since the numbers shared a common factor namely 2 I divided it out. Important "you cannot cancel out of a sum" meaning you cannot cancel a 2 with the 10 and leave the other 2. You must to cancel both of them whenever you deal with add/subt.