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Suppose p+q+r = 7 and p^2+q^2+r^2 = 9. Then, what is the average (arithmetic mean) of the three products pqqr, and rp?

 Jan 31, 2015

Best Answer 

 #1
avatar+26397 
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Suppose p+q+r = 7 and p^2+q^2+r^2 = 9.

Then, what is the average (arithmetic mean) of the three products  pqqr, and rp   ?

 (p+q+r)2=(p+q+r)(p+q+r)=p2+q2+r2+2(pq+qr+rp)(p+q+r)2=p2+q2+r2+2(pq+qr+rp)72=9+2(pq+qr+rp)2(pq+qr+rp)=729=499=40(pq+qr+rp)=20 

the average (arithmetic mean) of the three products  pqqr, and rp   ?   (pq+qr+rp)3=203=623

 Feb 1, 2015
 #1
avatar+26397 
+10
Best Answer

Suppose p+q+r = 7 and p^2+q^2+r^2 = 9.

Then, what is the average (arithmetic mean) of the three products  pqqr, and rp   ?

 (p+q+r)2=(p+q+r)(p+q+r)=p2+q2+r2+2(pq+qr+rp)(p+q+r)2=p2+q2+r2+2(pq+qr+rp)72=9+2(pq+qr+rp)2(pq+qr+rp)=729=499=40(pq+qr+rp)=20 

the average (arithmetic mean) of the three products  pqqr, and rp   ?   (pq+qr+rp)3=203=623

heureka Feb 1, 2015

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