anonymous
  • anonymous
if ab+1/ab=4, what is the value of a^2b^2+1/a^2b^2?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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zepdrix
  • zepdrix
The question is very unclear. Did you mean \(\large\rm ab+\frac{1}{ab}=4\) or \(\large\rm \frac{ab+1}{ab}=4\) ?
anonymous
  • anonymous
the first one
anonymous
  • anonymous
(ab) + 1/ab = 4

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zepdrix
  • zepdrix
Hmm I remember seeing this question before D: Trying to rememberrrr
anonymous
  • anonymous
I want to know the steps to solving it.
zepdrix
  • zepdrix
Well let's try this :) What happens when you square each side?\[\large\rm \left(ab+\frac{1}{ab}\right)^2=4^2\]Do you remember how to expand out a pair of binomials like this? Sometimes we call it FOIL'ing.
anonymous
  • anonymous
yes I know FOIL'ing
anonymous
  • anonymous
|dw:1446848427478:dw|
anonymous
  • anonymous
is AB X 1/AB= 1?
zepdrix
  • zepdrix
Yessss :) That's kind of an interesting thing happening with the middle terms, ya?
anonymous
  • anonymous
and is 1/AB X 1/AB = 1/A^2 B^2?
zepdrix
  • zepdrix
\[\large\rm \left(\frac{1}{ab}\right)\left(\frac{1}{ab}\right)\quad=\frac{1^2}{a^2b^2}\quad=\frac{1}{a^2b^2}\]Yup, looks good :)
anonymous
  • anonymous
\[A \frac{ ? }{ ? }\]
anonymous
  • anonymous
oops
anonymous
  • anonymous
|dw:1446848925917:dw|
anonymous
  • anonymous
is that correct?
zepdrix
  • zepdrix
So you moved the two 1's to the other side by subtraction? Yayyy good job! \c:/

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