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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?

Guest Jan 31, 2015

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 #1
avatar+18829 
+10

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   ?

$$\small{\text{
$
\begin{array}{rcl}
(p+q+r)^2&=&(p+q+r)(p+q+r)=p^2+q^2+r^2+2(pq+qr+rp)\\
(p+q+r)^2&=&p^2+q^2+r^2+2(pq+qr+rp)\\
7^2&=&9+2(pq+qr+rp)\\
2(pq+qr+rp)&=&7^2-9=49-9=40\\
(pq+qr+rp) &=& 20
\end{array}
$
}}$$

the average (arithmetic mean) of the three products  pqqr, and rp   ?   $$\frac{(pq+qr+rp) }{3} = \frac{20}{3}=6\frac{2}{3}$$

heureka  Feb 1, 2015
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1+0 Answers

 #1
avatar+18829 
+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   ?

$$\small{\text{
$
\begin{array}{rcl}
(p+q+r)^2&=&(p+q+r)(p+q+r)=p^2+q^2+r^2+2(pq+qr+rp)\\
(p+q+r)^2&=&p^2+q^2+r^2+2(pq+qr+rp)\\
7^2&=&9+2(pq+qr+rp)\\
2(pq+qr+rp)&=&7^2-9=49-9=40\\
(pq+qr+rp) &=& 20
\end{array}
$
}}$$

the average (arithmetic mean) of the three products  pqqr, and rp   ?   $$\frac{(pq+qr+rp) }{3} = \frac{20}{3}=6\frac{2}{3}$$

heureka  Feb 1, 2015

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