Question
(a) Show that the equation 3x^2-x^3+3=0 can be rearranged to give x=3+(3)/(x^2)
Answer
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Holly
Elite · Tutor for 8 years
Answer
The question wants you to show that
can be expressed in the form
. Our aim is to rearrange the equation to simplify it into a form with 'x' on the left-hand side of the equation and all the other quantities on the right.From
, we must move terms strategically. We'll start by moving the term
over to the right hand side. We do this by adding
on both sides of our equation to maintain mathematical integrity,which gives us:
Next, we shift the constant numeral , +3 to the right. This manipulation gives us the form:
From here, our next step is to isolate
. To do this, we express the right-side in the form of \((x^2 + \frac{1}{x^2})\). This procedure gives us
Then noticing that subtracting 2 after a sum essentially redistributes the '- 2' acrossthe terms inside the brackets so,
which simplifies to:
Finally seeing that
can be simplified as \(\frac{3}{-(1/x^2)}\) we replace
in
to
Which gives us:
To prove this accurate we can just plug whichever X value back into the equation and confirm that both sides equal.Please note that
as we have
in the denominator on the right-hand side.So we have managed, as the task asked us, to rearrange the given equation to the desired form.