Given that x is an integer such that
mula1" title="\x\sqrt{x}-5x-9\sqrt{x}=35[" alt="\x\sqrt{x}-5x-9\sqrt{x}=35[" align="absmiddle" class="latex-formula">, find x.
2 answers:
I have done this several times and do not find that x is an integer. I get an imaginary number. Crazy as it seems, here's what I got all 3 times I did this:
. That is definitely NOT an integer!
There appears to be a mistake in the LaTeX, so that the equation is supposed to be
If we let z=√x, then this is
By Descartes' rule of signs, this will have one positive real root. The rational root theorem says it will be one of 1, 5, 7, or 35. It is actually z=7. The corresponding value of x is
x = z² = 7² = 49.
A graphing calculator finds the solution to the original equation easily. (I find it useful to put it in the form f(x)=0.)
x = 49
If we let z=√x, then this is
By Descartes' rule of signs, this will have one positive real root. The rational root theorem says it will be one of 1, 5, 7, or 35. It is actually z=7. The corresponding value of x is
x = z² = 7² = 49.
A graphing calculator finds the solution to the original equation easily. (I find it useful to put it in the form f(x)=0.)
x = 49
You might be interested in
Let's split the problem in non-intersecting subsets: we have good wood racquets,
defective wood rackets,
good graphite racquets,
defective graphite rackets.
The probability that the racket is wood or defective covers the following subsets: good wood, defective wood and defective graphite, which have, respectively, ,
and
elements.
Since the total is elements, the probability is