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# Suppose and . Then, what is the average (arithmetic mean) of the three products , , and ?

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Suppose  and . Then, what is the average (arithmetic mean) of the three products , and ?

Jan 31, 2015

#1
+20831
+10

Suppose  and .

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

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

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

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Feb 1, 2015

#1
+20831
+10

Suppose  and .

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

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

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

heureka Feb 1, 2015