+0

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

0
269
1

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

Guest Jan 31, 2015

#1
+19191
+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
Sort:

#1
+19191
+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

### 8 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details