+0  
 
0
325
1
avatar

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

Best Answer 

 #1
avatar+19653 
+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
 #1
avatar+19653 
+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

5 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.