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avatar+245 

Given two real numbers 1 \(\frac{1}{p} + \frac{1}{q} = 1\) and  \(pq = \frac{9}{2}\), what is q?

 

I can't figure out how to do this.. i keep ending up only knowing what \(q^2+p^2\) is, which is -9/2. was i supposed to go that way?

 Jan 25, 2020
 #1
avatar+20747 
+2

Try this: 

Start with:                        pq  =  9/2

Divide both sides by q  :   p  =  9/(2q)

 

Substitute this into:               1/p + 1/q  =  1

 

                                    1/[9/(2q)] + 1/q  =  1

                                          2q/9  + 1/q  =  1

Multiply by 9q:                         2q2 + 9  =  9q

Rewrite:                            2q2 - 9q + 9  =  0

 

Now finish with factoring or the quadratic formula.

 Jan 25, 2020
 #2
avatar+245 
0

ah thank you ok so q=3 and p=3/2 right?

atlas9  Jan 25, 2020
 #3
avatar+20747 
+1

Since it's symmetrical, there are two answers:  q = 3 and p = 3/2  or  p = 3 and q = 3/2

 Jan 26, 2020

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